tutorials/T00-ToyDemonstration.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "56cea908-484d-47c8-a108-77a208ad1baa",
   "metadata": {},
   "source": [
    "# Toy Studies\n",
    "\n",
    "Application of the PAWS method on analytic distributions and pseudo datasets"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbfc0bbb-9d0a-4055-9276-6a301286e39f",
   "metadata": {},
   "source": [
    "## Part I - Formulation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d653046c-6528-4efc-953c-e64c1757566e",
   "metadata": {},
   "source": [
    "Given the feature vectors $\\vec{x}$ and the physics parameters $\\theta$, the output the supervised classifier approximates the posterior probability of signal ($y = 1$):\n",
    "\n",
    "$$f_{\\text{FS}}(\\vec{x}, \\theta) \\approx \\frac{P_S(\\vec{x}|\\theta)P_S(\\theta)}{P_S(\\vec{x}|\\theta)P_S(\\theta) + P_B(\\vec{x}|\\theta)P_B(\\theta)}$$\n",
    "\n",
    "where $S$ = Signal ($y = 1$) and $B$ = Background ($y = 0$).\n",
    "\n",
    "It is related to the likelihood ratio by\n",
    "\n",
    "$$\\Lambda_{\\text{FS}}(\\vec{x}, \\theta) \\equiv \\frac{P_S(\\vec{x}|\\theta)}{P_b(\\vec{x}|\\theta)} = \\kappa(\\theta) \\frac{f_{\\text{FS}}(\\vec{x}, \\theta)}{1 - f_{\\text{FS}}(\\vec{x}, \\theta)}$$\n",
    "\n",
    "where $\\kappa(\\theta) \\equiv P_B(\\theta) / P_S(\\theta)$  is the prior ratio between background and signal\n",
    "\n",
    "Similarly for the weakly supervised model:\n",
    "\n",
    "$$f_{\\text{WS}}(\\vec{x}, \\theta) = \\frac{P_D(\\vec{x}|\\theta)P_D(\\theta)}{P_D(\\vec{x}|\\theta)P_D(\\theta) + P_R(\\vec{x}|\\theta)P_R(\\theta)}$$\n",
    "\n",
    "where $D$ = Data and $R$ = Reference (= Background).\n",
    "\n",
    "Observe that when $\\theta = \\hat{\\theta}$ the data densities can be expressed in terms of the signal and background densities:\n",
    "\n",
    "$$P_D(\\vec{x}) = \\mu P_S(\\vec{x}) + (1 - \\mu) P_B(\\vec{x})$$\n",
    "\n",
    "The prior probabilities of data $P_D$ and reference $P_R$ can be related by:\n",
    "\n",
    "$$P_D = P_S + P_B = \\frac{\\mu}{1 - \\mu} P_R + P_R = \\frac{1}{1 - \\mu} P_R$$\n",
    "\n",
    "Expanding terms gives:\n",
    "\n",
    "$$f_{\\text{WS}}(\\vec{x}, \\theta) = \\dfrac{\\mu\\kappa(\\theta)\\dfrac{f_{\\text{FS}}(\\vec{x}, \\theta)}{1 - f_{\\text{FS}}(\\vec{x}, \\theta)} + 1 - \\mu}{\\mu\\kappa(\\theta)\\dfrac{f_{\\text{FS}}(\\vec{x}, \\theta)}{1 - f_{\\text{FS}}(\\vec{x}, \\theta)} + 2(1-\\mu)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e838742-413f-45e3-88d6-2dabd056b7b0",
   "metadata": {},
   "source": [
    "## Part II - Demonstration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cc595f58-16df-4f71-87a1-1c2a00f2e6d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "from collections import defaultdict\n",
    "from itertools import repeat\n",
    "from concurrent.futures import ProcessPoolExecutor\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy.stats import multivariate_normal, expon\n",
    "from scipy.optimize import minimize, minimize_scalar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "015c096b-f9fd-46cd-b851-06bcea95669b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_R(model_B, N_B, seed=None):\n",
    "    random_state = np.random.RandomState(seed) if seed is not None else None\n",
    "    return model_B.rvs(size=N_B, random_state=random_state)\n",
    "\n",
    "def get_D(model_S, model_B, N_B, mu_inj, seed=None):\n",
    "    N_S = int(mu_inj / (1 - mu_inj) * N_B)\n",
    "    random_state = np.random.RandomState(seed + 1) if seed is not None else None\n",
    "    return np.concatenate([model_S.rvs(size=N_S, random_state=random_state),\n",
    "                           model_B.rvs(size=N_B, random_state=random_state)])\n",
    "\n",
    "def get_pS_over_pB(x, model_S, model_B):\n",
    "    return model_S.pdf(x) / model_B.pdf(x)\n",
    "\n",
    "def get_FS(x, model_S, model_B):\n",
    "    pS_over_pB = get_pS_over_pB(x, model_S, model_B)\n",
    "    return pS_over_pB / (1 - pS_over_pB)\n",
    "\n",
    "def get_WS(x, mu, model_S, model_B):\n",
    "    pS_over_pB = get_pS_over_pB(x, model_S, model_B)\n",
    "    return (mu * pS_over_pB + 1 - mu) / (mu * pS_over_pB + 2 - 2 * mu)\n",
    "\n",
    "def get_BCE(x, y, mu, model_S, model_B):\n",
    "    WS = get_WS(x, mu, model_S, model_B)\n",
    "    overflow = (1 - WS) <= 0.\n",
    "    underflow = WS <= 0.\n",
    "    WS[overflow] = 1 - 1e-6\n",
    "    WS[underflow] = 1e-6\n",
    "    return - y * np.log(WS) - (1. - y) * np.log(1. - WS )\n",
    "\n",
    "def get_total_loss(D, R, mu, model_S, model_B):\n",
    "    y = np.concatenate([np.ones(D.shape[0]), np.zeros(R.shape[0])])\n",
    "    x = np.concatenate([D, R])\n",
    "    return np.mean(get_BCE(x, y, mu, model_S, model_B))\n",
    "\n",
    "def get_loss_over_mu(D, R, mu_list, model_S, model_B):\n",
    "    data = []\n",
    "    for mu in mu_list:\n",
    "        data.append({\n",
    "            'mu': mu,\n",
    "            'loss': get_total_loss(D, R, mu, model_S, model_B)\n",
    "        })\n",
    "    return data\n",
    "\n",
    "def run_trial(mu, trial, N_B, model_S, model_B):\n",
    "    sys.stdout.write(f'Running trial {trial + 1} with mu = {mu}\\n')\n",
    "    R = get_R(model_B, N_B, seed=trial)\n",
    "    D = get_D(model_S, model_B, N_B, mu, seed=trial)\n",
    "    func = lambda x : get_total_loss(D, R, x, model_S, model_B)\n",
    "    #func = lambda x : np.mean(get_BCE(D, 1 , x, model_S, model_B)) + np.mean(get_BCE(R, 0 , x, model_S, model_B))\n",
    "    res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
    "    mu_hat = res.x\n",
    "    return [mu, mu_hat]\n",
    "\n",
    "def scan_mu_hat(mu_list, N_B, N_trial, model_S, model_B, max_workers=None):\n",
    "    mu_args = np.repeat(mu_list, N_trial)\n",
    "    trial_args = np.tile(np.arange(N_trial), len(mu_args))\n",
    "    outputs = []\n",
    "    if max_workers == 0:\n",
    "        for mu, trial in zip(mu_args, trial_args):\n",
    "            outputs.append(run_trial(mu, trial, N_B, model_S, model_B))\n",
    "    else:\n",
    "        with ProcessPoolExecutor(max_workers=max_workers) as executor:\n",
    "            outputs = list(executor.map(run_trial, mu_args, trial_args, repeat(N_B), repeat(model_S), repeat(model_B)))\n",
    "    outputs = np.array(outputs)\n",
    "    result = defaultdict(list)\n",
    "    for output in outputs:\n",
    "        result[output[0]].append(output[1])\n",
    "    return result\n",
    "\n",
    "def create_mu_plot(mu_hats, title: str = ''):\n",
    "    mu_trues = np.array(list(mu_hats))\n",
    "    mu_hats = np.array([values for values in mu_hats.values()])\n",
    "    mu_mean = np.mean(mu_hats, axis=1)\n",
    "    mu_std = np.std(mu_hats, axis=1)\n",
    "    plt.fill_between(mu_trues, mu_mean - mu_std, mu_mean + mu_std, alpha=0.2)\n",
    "    plt.plot(mu_trues, mu_mean)\n",
    "    plt.plot(mu_trues, mu_trues, linestyle=\":\", color=\"gray\")\n",
    "    plt.xscale(\"log\")\n",
    "    plt.yscale(\"log\")\n",
    "    plt.xlabel(\"True $\\mu$\")\n",
    "    plt.ylabel(\"Fitted $\\mu$\")\n",
    "    plt.title(title)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81a76bf8-f17f-497a-9aa3-b3197ba43648",
   "metadata": {},
   "source": [
    "### Analytic Distributions - 1D Gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "40e9fe02-bb9f-4275-807b-720507a63255",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running trial 1 with mu = 0.01\n",
      "Running trial 3 with mu = 0.01\n",
      "Running trial 2 with mu = 0.01\n",
      "Running trial 4 with mu = 0.01\n",
      "Running trial 5 with mu = 0.01\n",
      "Running trial 6 with mu = 0.01\n",
      "Running trial 7 with mu = 0.01\n",
      "Running trial 8 with mu = 0.01\n",
      "Running trial 9 with mu = 0.01\n",
      "Running trial 10 with mu = 0.01\n",
      "Running trial 1 with mu = 0.015448591479026755\n",
      "Running trial 2 with mu = 0.015448591479026755\n",
      "Running trial 3 with mu = 0.015448591479026755\n",
      "Running trial 4 with mu = 0.015448591479026755\n",
      "Running trial 5 with mu = 0.015448591479026755\n",
      "Running trial 10 with mu = 0.015448591479026755\n",
      "Running trial 9 with mu = 0.015448591479026755\n",
      "Running trial 2 with mu = 0.023865897868585808\n",
      "Running trial 7 with mu = 0.015448591479026755\n",
      "Running trial 4 with mu = 0.023865897868585808\n",
      "Running trial 1 with mu = 0.023865897868585808\n",
      "Running trial 3 with mu = 0.023865897868585808\n",
      "Running trial 8 with mu = 0.015448591479026755\n",
      "Running trial 5 with mu = 0.023865897868585808\n",
      "Running trial 6 with mu = 0.015448591479026755\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running trial 6 with mu = 0.023865897868585808\n",
      "Running trial 7 with mu = 0.023865897868585808\n",
      "Running trial 8 with mu = 0.023865897868585808\n",
      "Running trial 9 with mu = 0.023865897868585808\n",
      "Running trial 10 with mu = 0.023865897868585808\n",
      "Running trial 2 with mu = 0.036869450645195756\n",
      "Running trial 3 with mu = 0.036869450645195756\n",
      "Running trial 4 with mu = 0.036869450645195756\n",
      "Running trial 1 with mu = 0.036869450645195756\n",
      "Running trial 7 with mu = 0.036869450645195756\n",
      "Running trial 5 with mu = 0.036869450645195756\n",
      "Running trial 6 with mu = 0.036869450645195756\n",
      "Running trial 10 with mu = 0.036869450645195756\n",
      "Running trial 9 with mu = 0.036869450645195756\n",
      "Running trial 1 with mu = 0.056958108107376865\n",
      "Running trial 8 with mu = 0.036869450645195756\n",
      "Running trial 2 with mu = 0.056958108107376865\n",
      "Running trial 5 with mu = 0.056958108107376865\n",
      "Running trial 4 with mu = 0.056958108107376865\n",
      "Running trial 7 with mu = 0.056958108107376865\n",
      "Running trial 6 with mu = 0.056958108107376865\n",
      "Running trial 8 with mu = 0.056958108107376865\n",
      "Running trial 9 with mu = 0.056958108107376865\n",
      "Running trial 3 with mu = 0.056958108107376865\n",
      "Running trial 10 with mu = 0.056958108107376865\n",
      "Running trial 1 with mu = 0.0879922543569107\n",
      "Running trial 2 with mu = 0.0879922543569107\n",
      "Running trial 3 with mu = 0.0879922543569107\n",
      "Running trial 4 with mu = 0.0879922543569107\n",
      "Running trial 5 with mu = 0.0879922543569107\n",
      "Running trial 6 with mu = 0.0879922543569107\n",
      "Running trial 7 with mu = 0.0879922543569107\n",
      "Running trial 8 with mu = 0.0879922543569107\n",
      "Running trial 9 with mu = 0.0879922543569107\n",
      "Running trial 1 with mu = 0.13593563908785256\n",
      "Running trial 10 with mu = 0.0879922543569107\n",
      "Running trial 2 with mu = 0.13593563908785256\n",
      "Running trial 3 with mu = 0.13593563908785256\n",
      "Running trial 4 with mu = 0.13593563908785256\n",
      "Running trial 5 with mu = 0.13593563908785256\n",
      "Running trial 7 with mu = 0.13593563908785256\n",
      "Running trial 6 with mu = 0.13593563908785256\n",
      "Running trial 8 with mu = 0.13593563908785256\n",
      "Running trial 9 with mu = 0.13593563908785256\n",
      "Running trial 10 with mu = 0.13593563908785256\n",
      "Running trial 1 with mu = 0.21000141557086555\n",
      "Running trial 2 with mu = 0.21000141557086555\n",
      "Running trial 3 with mu = 0.21000141557086555\n",
      "Running trial 4 with mu = 0.21000141557086555\n",
      "Running trial 5 with mu = 0.21000141557086555\n",
      "Running trial 6 with mu = 0.21000141557086555\n",
      "Running trial 7 with mu = 0.21000141557086555\n",
      "Running trial 8 with mu = 0.21000141557086555\n",
      "Running trial 9 with mu = 0.21000141557086555\n",
      "Running trial 10 with mu = 0.21000141557086555\n",
      "Running trial 1 with mu = 0.324422607917163\n",
      "Running trial 2 with mu = 0.324422607917163\n",
      "Running trial 3 with mu = 0.324422607917163\n",
      "Running trial 5 with mu = 0.324422607917163\n",
      "Running trial 6 with mu = 0.324422607917163\n",
      "Running trial 7 with mu = 0.324422607917163\n",
      "Running trial 8 with mu = 0.324422607917163\n",
      "Running trial 4 with mu = 0.324422607917163\n",
      "Running trial 10 with mu = 0.324422607917163\n",
      "Running trial 9 with mu = 0.324422607917163\n",
      "Running trial 1 with mu = 0.5011872336272722\n",
      "Running trial 2 with mu = 0.5011872336272722\n",
      "Running trial 3 with mu = 0.5011872336272722\n",
      "Running trial 4 with mu = 0.5011872336272722\n",
      "Running trial 5 with mu = 0.5011872336272722\n",
      "Running trial 6 with mu = 0.5011872336272722\n",
      "Running trial 7 with mu = 0.5011872336272722\n",
      "Running trial 8 with mu = 0.5011872336272722\n",
      "Running trial 9 with mu = 0.5011872336272722\n",
      "Running trial 10 with mu = 0.5011872336272722\n"
     ]
    }
   ],
   "source": [
    "mu_inj_list = np.logspace(-2, -0.3, 10)\n",
    "N_trial = 10\n",
    "N_B = 100000\n",
    "seed = 2024\n",
    "\n",
    "mu_S = 3\n",
    "mu_B = 6\n",
    "sigma = 1\n",
    "\n",
    "model_S = multivariate_normal(mean=mu_S, cov=sigma, seed=seed)\n",
    "model_B = multivariate_normal(mean=mu_B, cov=sigma, seed=seed)\n",
    "\n",
    "mu_hats = scan_mu_hat(mu_inj_list, N_B, N_trial, model_S, model_B, max_workers=25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5dd57f04-4eb3-4110-b9b7-9795bf6f26c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_mu_plot(mu_hats, title='1D Gaussian Case')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dff74789-653a-45ff-8a33-7e36b584b7bf",
   "metadata": {},
   "source": [
    "### Analytic Distributions - 3D Gaussian (Uncorrelated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c32c7caf-d216-44ac-bcd3-3ec14ca874ae",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running trial 1 with mu = 0.01\n",
      "Running trial 2 with mu = 0.01\n",
      "Running trial 3 with mu = 0.01\n",
      "Running trial 4 with mu = 0.01\n",
      "Running trial 5 with mu = 0.01\n",
      "Running trial 6 with mu = 0.01\n",
      "Running trial 7 with mu = 0.01\n",
      "Running trial 8 with mu = 0.01\n",
      "Running trial 9 with mu = 0.01\n",
      "Running trial 10 with mu = 0.01\n",
      "Running trial 1 with mu = 0.015448591479026755\n",
      "Running trial 2 with mu = 0.015448591479026755\n",
      "Running trial 3 with mu = 0.015448591479026755\n",
      "Running trial 4 with mu = 0.015448591479026755\n",
      "Running trial 5 with mu = 0.015448591479026755\n",
      "Running trial 6 with mu = 0.015448591479026755\n",
      "Running trial 7 with mu = 0.015448591479026755\n",
      "Running trial 8 with mu = 0.015448591479026755\n",
      "Running trial 9 with mu = 0.015448591479026755\n",
      "Running trial 10 with mu = 0.015448591479026755\n",
      "Running trial 1 with mu = 0.023865897868585808\n",
      "Running trial 2 with mu = 0.023865897868585808\n",
      "Running trial 3 with mu = 0.023865897868585808\n",
      "Running trial 4 with mu = 0.023865897868585808\n",
      "Running trial 5 with mu = 0.023865897868585808\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running trial 6 with mu = 0.023865897868585808\n",
      "Running trial 7 with mu = 0.023865897868585808\n",
      "Running trial 8 with mu = 0.023865897868585808\n",
      "Running trial 9 with mu = 0.023865897868585808\n",
      "Running trial 10 with mu = 0.023865897868585808\n",
      "Running trial 1 with mu = 0.036869450645195756\n",
      "Running trial 2 with mu = 0.036869450645195756\n",
      "Running trial 3 with mu = 0.036869450645195756\n",
      "Running trial 4 with mu = 0.036869450645195756\n",
      "Running trial 5 with mu = 0.036869450645195756\n",
      "Running trial 6 with mu = 0.036869450645195756\n",
      "Running trial 8 with mu = 0.036869450645195756\n",
      "Running trial 7 with mu = 0.036869450645195756\n",
      "Running trial 9 with mu = 0.036869450645195756\n",
      "Running trial 10 with mu = 0.036869450645195756\n",
      "Running trial 1 with mu = 0.056958108107376865\n",
      "Running trial 2 with mu = 0.056958108107376865\n",
      "Running trial 3 with mu = 0.056958108107376865\n",
      "Running trial 4 with mu = 0.056958108107376865\n",
      "Running trial 5 with mu = 0.056958108107376865\n",
      "Running trial 6 with mu = 0.056958108107376865\n",
      "Running trial 7 with mu = 0.056958108107376865\n",
      "Running trial 8 with mu = 0.056958108107376865\n",
      "Running trial 9 with mu = 0.056958108107376865\n",
      "Running trial 10 with mu = 0.056958108107376865\n",
      "Running trial 1 with mu = 0.0879922543569107\n",
      "Running trial 2 with mu = 0.0879922543569107\n",
      "Running trial 3 with mu = 0.0879922543569107\n",
      "Running trial 4 with mu = 0.0879922543569107\n",
      "Running trial 5 with mu = 0.0879922543569107\n",
      "Running trial 6 with mu = 0.0879922543569107\n",
      "Running trial 7 with mu = 0.0879922543569107\n",
      "Running trial 8 with mu = 0.0879922543569107\n",
      "Running trial 9 with mu = 0.0879922543569107\n",
      "Running trial 10 with mu = 0.0879922543569107\n",
      "Running trial 1 with mu = 0.13593563908785256\n",
      "Running trial 2 with mu = 0.13593563908785256\n",
      "Running trial 3 with mu = 0.13593563908785256\n",
      "Running trial 4 with mu = 0.13593563908785256\n",
      "Running trial 5 with mu = 0.13593563908785256\n",
      "Running trial 6 with mu = 0.13593563908785256\n",
      "Running trial 7 with mu = 0.13593563908785256\n",
      "Running trial 8 with mu = 0.13593563908785256\n",
      "Running trial 9 with mu = 0.13593563908785256\n",
      "Running trial 10 with mu = 0.13593563908785256\n",
      "Running trial 1 with mu = 0.21000141557086555\n",
      "Running trial 2 with mu = 0.21000141557086555\n",
      "Running trial 3 with mu = 0.21000141557086555\n",
      "Running trial 4 with mu = 0.21000141557086555\n",
      "Running trial 5 with mu = 0.21000141557086555\n",
      "Running trial 6 with mu = 0.21000141557086555\n",
      "Running trial 7 with mu = 0.21000141557086555\n",
      "Running trial 8 with mu = 0.21000141557086555\n",
      "Running trial 9 with mu = 0.21000141557086555\n",
      "Running trial 10 with mu = 0.21000141557086555\n",
      "Running trial 1 with mu = 0.324422607917163\n",
      "Running trial 2 with mu = 0.324422607917163\n",
      "Running trial 3 with mu = 0.324422607917163\n",
      "Running trial 4 with mu = 0.324422607917163\n",
      "Running trial 5 with mu = 0.324422607917163\n",
      "Running trial 6 with mu = 0.324422607917163\n",
      "Running trial 7 with mu = 0.324422607917163\n",
      "Running trial 8 with mu = 0.324422607917163\n",
      "Running trial 9 with mu = 0.324422607917163\n",
      "Running trial 10 with mu = 0.324422607917163\n",
      "Running trial 1 with mu = 0.5011872336272722\n",
      "Running trial 2 with mu = 0.5011872336272722\n",
      "Running trial 3 with mu = 0.5011872336272722\n",
      "Running trial 4 with mu = 0.5011872336272722\n",
      "Running trial 5 with mu = 0.5011872336272722\n",
      "Running trial 6 with mu = 0.5011872336272722\n",
      "Running trial 7 with mu = 0.5011872336272722\n",
      "Running trial 8 with mu = 0.5011872336272722\n",
      "Running trial 9 with mu = 0.5011872336272722\n",
      "Running trial 10 with mu = 0.5011872336272722\n"
     ]
    }
   ],
   "source": [
    "mu_inj_list = np.logspace(-2, -0.3, 10)\n",
    "N_trial = 10\n",
    "N_B = 200000\n",
    "seed = 2024\n",
    "\n",
    "mu_S = [1, 3, 5]\n",
    "mu_B = [6, 4, 2]\n",
    "sigma = 1\n",
    "\n",
    "model_S = multivariate_normal(mean=mu_S, cov=sigma, seed=seed)\n",
    "model_B = multivariate_normal(mean=mu_B, cov=sigma, seed=seed)\n",
    "\n",
    "mu_hats = scan_mu_hat(mu_inj_list, N_B, N_trial, model_S, model_B, max_workers=25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "80155461-f655-49aa-b073-057f505247c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_mu_plot(mu_hats, title='3D Gaussian Case')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f88e41b-81d0-4b89-aae7-10f428fac0b4",
   "metadata": {},
   "source": [
    "### Analytic Distributions - 2D Gaussian (Correlated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "68f71b0e-28f4-4bb4-b083-53c7824c6cd8",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running trial 1 with mu = 0.01\n",
      "Running trial 2 with mu = 0.01\n",
      "Running trial 3 with mu = 0.01\n",
      "Running trial 4 with mu = 0.01\n",
      "Running trial 5 with mu = 0.01\n",
      "Running trial 6 with mu = 0.01\n",
      "Running trial 7 with mu = 0.01\n",
      "Running trial 8 with mu = 0.01\n",
      "Running trial 9 with mu = 0.01\n",
      "Running trial 10 with mu = 0.01\n",
      "Running trial 1 with mu = 0.015448591479026755\n",
      "Running trial 2 with mu = 0.015448591479026755\n",
      "Running trial 3 with mu = 0.015448591479026755\n",
      "Running trial 4 with mu = 0.015448591479026755\n",
      "Running trial 5 with mu = 0.015448591479026755\n",
      "Running trial 6 with mu = 0.015448591479026755\n",
      "Running trial 7 with mu = 0.015448591479026755\n",
      "Running trial 8 with mu = 0.015448591479026755\n",
      "Running trial 9 with mu = 0.015448591479026755\n",
      "Running trial 10 with mu = 0.015448591479026755\n",
      "Running trial 1 with mu = 0.023865897868585808\n",
      "Running trial 2 with mu = 0.023865897868585808\n",
      "Running trial 3 with mu = 0.023865897868585808\n",
      "Running trial 4 with mu = 0.023865897868585808\n",
      "Running trial 5 with mu = 0.023865897868585808\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running trial 6 with mu = 0.023865897868585808\n",
      "Running trial 7 with mu = 0.023865897868585808\n",
      "Running trial 8 with mu = 0.023865897868585808\n",
      "Running trial 9 with mu = 0.023865897868585808\n",
      "Running trial 10 with mu = 0.023865897868585808\n",
      "Running trial 1 with mu = 0.036869450645195756\n",
      "Running trial 2 with mu = 0.036869450645195756\n",
      "Running trial 3 with mu = 0.036869450645195756\n",
      "Running trial 4 with mu = 0.036869450645195756\n",
      "Running trial 5 with mu = 0.036869450645195756\n",
      "Running trial 6 with mu = 0.036869450645195756\n",
      "Running trial 7 with mu = 0.036869450645195756\n",
      "Running trial 8 with mu = 0.036869450645195756\n",
      "Running trial 9 with mu = 0.036869450645195756\n",
      "Running trial 10 with mu = 0.036869450645195756\n",
      "Running trial 2 with mu = 0.056958108107376865\n",
      "Running trial 1 with mu = 0.056958108107376865\n",
      "Running trial 3 with mu = 0.056958108107376865\n",
      "Running trial 4 with mu = 0.056958108107376865\n",
      "Running trial 5 with mu = 0.056958108107376865\n",
      "Running trial 6 with mu = 0.056958108107376865\n",
      "Running trial 7 with mu = 0.056958108107376865\n",
      "Running trial 8 with mu = 0.056958108107376865\n",
      "Running trial 9 with mu = 0.056958108107376865\n",
      "Running trial 10 with mu = 0.056958108107376865\n",
      "Running trial 1 with mu = 0.0879922543569107\n",
      "Running trial 2 with mu = 0.0879922543569107\n",
      "Running trial 3 with mu = 0.0879922543569107\n",
      "Running trial 4 with mu = 0.0879922543569107\n",
      "Running trial 5 with mu = 0.0879922543569107\n",
      "Running trial 6 with mu = 0.0879922543569107\n",
      "Running trial 7 with mu = 0.0879922543569107\n",
      "Running trial 8 with mu = 0.0879922543569107\n",
      "Running trial 9 with mu = 0.0879922543569107\n",
      "Running trial 10 with mu = 0.0879922543569107\n",
      "Running trial 1 with mu = 0.13593563908785256\n",
      "Running trial 2 with mu = 0.13593563908785256\n",
      "Running trial 3 with mu = 0.13593563908785256\n",
      "Running trial 4 with mu = 0.13593563908785256\n",
      "Running trial 5 with mu = 0.13593563908785256\n",
      "Running trial 6 with mu = 0.13593563908785256\n",
      "Running trial 7 with mu = 0.13593563908785256\n",
      "Running trial 8 with mu = 0.13593563908785256\n",
      "Running trial 9 with mu = 0.13593563908785256\n",
      "Running trial 10 with mu = 0.13593563908785256\n",
      "Running trial 1 with mu = 0.21000141557086555\n",
      "Running trial 2 with mu = 0.21000141557086555\n",
      "Running trial 3 with mu = 0.21000141557086555\n",
      "Running trial 4 with mu = 0.21000141557086555\n",
      "Running trial 5 with mu = 0.21000141557086555\n",
      "Running trial 6 with mu = 0.21000141557086555\n",
      "Running trial 7 with mu = 0.21000141557086555\n",
      "Running trial 8 with mu = 0.21000141557086555\n",
      "Running trial 9 with mu = 0.21000141557086555\n",
      "Running trial 10 with mu = 0.21000141557086555\n",
      "Running trial 1 with mu = 0.324422607917163\n",
      "Running trial 2 with mu = 0.324422607917163\n",
      "Running trial 3 with mu = 0.324422607917163\n",
      "Running trial 4 with mu = 0.324422607917163\n",
      "Running trial 5 with mu = 0.324422607917163\n",
      "Running trial 6 with mu = 0.324422607917163\n",
      "Running trial 7 with mu = 0.324422607917163\n",
      "Running trial 8 with mu = 0.324422607917163\n",
      "Running trial 9 with mu = 0.324422607917163\n",
      "Running trial 10 with mu = 0.324422607917163\n",
      "Running trial 1 with mu = 0.5011872336272722\n",
      "Running trial 2 with mu = 0.5011872336272722\n",
      "Running trial 3 with mu = 0.5011872336272722\n",
      "Running trial 4 with mu = 0.5011872336272722\n",
      "Running trial 5 with mu = 0.5011872336272722\n",
      "Running trial 6 with mu = 0.5011872336272722\n",
      "Running trial 7 with mu = 0.5011872336272722\n",
      "Running trial 8 with mu = 0.5011872336272722\n",
      "Running trial 9 with mu = 0.5011872336272722\n",
      "Running trial 10 with mu = 0.5011872336272722\n"
     ]
    }
   ],
   "source": [
    "mu_inj_list = np.logspace(-2, -0.3, 10)\n",
    "N_trial = 10\n",
    "N_B = 100000\n",
    "seed = 2024\n",
    "\n",
    "mu_S = [1, 3]\n",
    "mu_B = [1.5, 3.5]\n",
    "cov_S = np.array([[5, 4.5], [4.5, 5]]) # High Positive Correlation\n",
    "cov_B = np.array([[3, -2.7], [-2.7, 3]]) # Positive Correlation\n",
    "sigma = 1\n",
    "\n",
    "model_S = multivariate_normal(mean=mu_S, cov=cov_S, seed=seed)\n",
    "model_B = multivariate_normal(mean=mu_B, cov=cov_B, seed=seed)\n",
    "\n",
    "mu_hats = scan_mu_hat(mu_inj_list, N_B, N_trial, model_S, model_B, max_workers=25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0a81442e-80b9-48fd-852d-9213460148b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4+uqryc7O5pprrmH//v2MHTuWtWvXcu+993L++eczf/78E37tWVlZ/PKXv+TnP/85e/fu5dxzzyUuLo7CwkLWrVvXOMPRkmnTphEXF8fNN9/ML37xC+x2Oy+88AJbt25tNvZYwLn//vs577zzsFqtjBs3jnPOOYdvfvObXHfddWzYsIGZM2cSERHB4cOHWbt2LWPHjuVb3/oWcXFx3HbbbfzqV7/ixhtv5LLLLiMvL4+77rqrXa00qJ+9WLRoEfPnz+faa69l0aJFJCcn4/V62bZtG2+++SbR0dGN4y+44AKWLl3K1772Nb75zW9SUlLCQw891OLM1lVXXcUdd9zBnXfeyaxZs9ixYwePP/54s2uWpk6dyoUXXsi4ceOIi4vj008/5fnnn+fss8/G4/Gwbds2vv3tb3PZZZcxdOhQHA4Hq1atYtu2bW3O0HSk1pNhtVr55z//ycKFCzn77LP51re+xZw5c4iIiODAgQO8/PLLvPrqq5SVlQH1wffZZ59lxIgRjBs3jo0bN/Lggw+Snp7e5LwXXXQRY8aMYcqUKSQlJXHgwAEeffRRBgwYwNChQwH47W9/y/Tp05kxYwbf+ta3yMrKorKykt27d/Pqq6823gUp0qquvfZbpOeYNWtWi+vsHPvV1tiIiAhz0KBB5qWXXmr+/e9/N0OhUIee+1//+pd5wQUXmElJSabNZjPj4uLMOXPmmE899ZQZCAQax5WUlJg333yz2b9/f9Nms5kDBgwwf/rTn7a6jtEXHbsrbf369S3WsWzZMnPOnDlmdHS06XQ6zQEDBpiXXnqp+eabbzaOaemutPfff988++yzTY/HYyYlJZk33nijuWnTJhMw//znPzeOCwQC5o033mgmJSWZhmE0WcfINOsXx5w6daoZERFhut1uc/DgwebVV1/d5K7AcDhs3nfffWZGRobpcDjMcePGma+++mq7F3g0TdP0+/3mY489Zk6fPt2MjY01bTabGR8fb86YMcO8//77zZKSkibj//SnP5nDhw83nU6nOWjQIPO+++4z//jHPzarPxAImD/60Y/MjIwM0+12m7NmzTK3bNnS7K60n/zkJ+aUKVPMuLi4xnN+//vfN4uLi03TrF9s9NprrzVHjBhhRkREmJGRkea4cePMRx55pMkdcy295vbWemwdoy/qyJ9jeXm5ec8995iTJk0yIyMjTbvdbmZmZppXXnml+d577zWOKysrM2+44QYzOTnZ9Hg85vTp0801a9Y0e66HH37YnDZtmpmYmGg6HA4zMzPTvOGGG5qtB7Zv3z7z+uuvN9PS0ky73W4mJSWZ06ZNM3/1q1+1q27p2wzTPAW3x4iIiIj0QLrGSERERKSBgpGIiIhIAwUjERERkQYKRiIiIiINFIxEREREGigYiYiIiDTQAo8dEA6HKSgoICoq6rjbM4iIiEj3YJomlZWVpKamYrG0PSekYNQBBQUFZGRkdHUZIiIicgLy8vKaraj+RQpGHRAVFQXU/8F+fksAERER6b68Xi8ZGRmNn+NtUTBqh+zsbLKzswmFQgBER0crGImIiPQw7bkMRluCdIDX6yUmJoaKigoFIxERkR6iI5/fuitNREREpIGCkYiIiEgDBSMRERGRBgpGIiIiIg0UjEREREQaKBiJiIiINFAwEhEREWmgYCQiIiLSQMFIREREpIGCkYiIiEgDBSMRERGRBgpGIiIi0i0UlPvIOVLZpTUoGImIiEiXe+Pjw5z76Lvc/L8bqQ4Eu6wOW5c9cw+SnZ1NdnY2oVCoq0sRERHpVar8tdzz6nZe2lgAwMDECLz+OiKcXRNRDNM0zS555h7I6/USExNDRUUF0dHRXV2OiIhIj7YuJ4//+9s/OFzr4KO6Adw0axA/WDgcu7VzG1od+fzWjJGIiIicVuGwyZ/e28dzyz9ivr2CCJuVb152AXPHDejq0hSMRERE5PQpqvSz5KWtrN1dDERTmjKG739lOllpKV1dGqBgJCIiIqfJqx9+yhvLV7DOl4XT5uCOC0fy9akDMAyjq0trpGAkIiIip5S/LsRvXt9B+aY3SLH4mBddyJIbrmBoSlRXl9aMgpGIiIicMrsKK7nlr5vILawiwcjiopQKfn3t5cTHdr9QBApGIiIicgqYpsnvX/uQFz7az4G6aOI8dh766mzmjEju6tLapGAkIiIinaqsupY7/rKSxMINTLPayEo7hwe/fhbJUa6uLu24FIxERESk07y/u5jvvriFkqowFzo9ZKSncdfV03A6HV1dWrsoGImIiMhJqwuFeeDltfxhsxcTg6yESK6/7DomZCV2dWkdomAkIiIiJ2Xf0Soe+sNfSa49zGBrFpMmTuCuL43G4+h5MaPnVSwiIiLdgmma/GNjPnf8eztDwhaSbHDFxCRuuHR8V5d2whSMREREpMMqfLX8/OXN/Gd7MQCOzJF8Zf48xg0b2MWVnRwFIxEREemQ93ce4q9/e5naYAiLMYzvzhvGt+cOxWrpPitYnygFIxEREWmXUNjkd2/t4rm3t3Ghw4vFCn+8eBhzJg7r6tI6jYKRiIiIHNehch/f+esmNh0sB9zUpE7i1vMnkpWe2tWldSoFIxEREWnTy+/t4O2V/2V3YABuewS/WjyGSyand3VZp4SCkYiIiLSopjbIHcs+oeKT1WRYK5kfWcB3b76eAQkRXV3aKaNg1A7Z2dlkZ2cTCoW6uhQREZHT4uP8cm7562YOltYQwQAyU0u4/apLiY/rvaEIwDBN0+zqInoKr9dLTEwMFRUVREdHd3U5IiIinS4cNnn8Px/x2roccoKJJEU5+e3lE5g2pGetYP15Hfn81oyRiIiIAFDk9fPD598h6+iHTLUZDMxI474rZxIX0TP2OesMCkYiIiLCyh1HuO3v26jw1WFzxjEyNZafXn0ObnffCUWgYCQiItKn+etC3PN/q/nrjhpMLAxNjuKH/3MVw/vHYhg9f8HGjlIwEhER6aNyjni5/0//YEDdQSbZ+jFqyjn8/IKRuOzWri6tyygYiYiI9DGmafLn9/bzmzd20t+0M8AJ541O4YYvj+6Ts0Sfp2AkIiLSh5RUBbjt/9bx9h4vAGmDh/A/82czfGDvXLCxoxSMRERE+oi3Psnjb/9YRly4Grd1NN9bOIpvzBiEpRds/tpZFIxERER6udpgmN+88Sl/fW83X3JV4rYEeeyiTOafNbirS+t2FIxERER6sd2FlXz7/zaz80glYIOss7h2zjAGDlDrrCUKRiIiIr2QaZr85Z0drFu9nPLa/kQ547n3K2O4aHxaV5fWrSkYiYiI9DIVvjp++PetVOxazyhbJXM8Yb59y5dI6+X7nHUGBSMREZFe5MO9JXz3xc0UegM4jDTG9XPzg//5EokKRe2iYCQiItILBENhHlz2ER9u3k5hsD+pMS5+d8VEpmTFd3VpPYqCkYiISA+XV1LDd//3A0aXvc8ke5hBGf355TUziXLZu7q0HkfBSEREpAf7x6Z87lz2CdW1IezOFM5MsfHDq+bgUSg6IQpGIiIiPVCVv447X3ib/+zyUYuNUf2jufeKmQxKiuzz23qcDAUjERGRHmbjgVIeev41hgf3Mt0Ry8Az5vOT80dit1q6urQeT8FIRESkhwiHTX63ahePr9pNjOlkmMvg7GGpXH/+CKwKRZ1CwUhERKQHKCirYckLH/Jhvg+A0cOyuHbhTAam9+viynoXBSMREZFu7t+bDvLPV19loFnGTttYvrNoHNdPz9K1RKeAgpGIiEg35QsEuePf23ll40EucNbgtIS4b0EK580Y2NWl9VoKRiIiIt3Qx/nl3Pp/m9lXUgNYiBh+Dl+f2o+hgwd1dWm9moJRO2RnZ5OdnU0oFOrqUkREpJczTZMnVm5n23srsQXjiHGncu/FY7hgXGpXl9YnGKZpml1dRE/h9XqJiYmhoqKC6Ojori5HRER6mUKvnyV/20LZvh1MdeQRNOzc+K1bGJAU09Wl9Wgd+fzWjJGIiEg3sHL7EX7yyseUVNdis6QwvZ+Lm748j34KRaeVgpGIiEgX8teF+PUr68j9ZAuldRmkx3l45PIJnKHNX7uEgpGIiEgX+fSwlx+8uJGxFe8zyhYkIyWBO29YSLTb0dWl9VkKRiIiIqeZaZo8+/5+HvhvDr66EIYzk1mJPpZccx5RCkVdSsFIRETkNCquDHDHX9/hvf2V+EwXY9KieeSrMxiSHKUFG7sBBSMREZHT5O2dRfz25bcYH8xltsNDwqRF/PSCMThs2uesu1AwEhEROcX8dSEeXJ7Dn9/bh9N0MdptY8SAVG48b4RCUTejYCQiInIK5RZW8rP/+5ANR2oBmDosjesXnsOgtCS1zrohBSMREZFTIBw2+b+P9vPf5csZRREF9pFcM38SN04fiNWqWaLuSsFIRESkk5VUBbjjX9t5/eMCZjtqsVpNlpwdz6WzBnd1aXIcCkYiIiKdxDRN1u4+ys9f+YSDZT7AIHnU2XxlfAxjRw7r6vKkHRSMREREOoG/Lsjvlm8nZ/1qkkNOKj2D+MWXRvOlcalYLLqWqKdQMBIRETlJe4qq+Mkr2zhycB/zneWELRbuumoxYwb26+rSpIMUjERERE5QMBRm2eZD/Pr1TymrqcNujcORMZYrFpxBVoZCUU+kYCQiInICSqoC3PevjRTu3ERlXSaZ8VH8+uIxTB+SqNvwezAFIxERkQ4Ih00+2l/K7a9sY0zleobYfKTGR/KDGxeSHOXq6vLkJCkYiYiItFNNIMgf1u4j++3dBIJhws6BLIot5ltfv0ihqJdQMBIREWmHPUcruffvH/JxfgmBcBTj0mP49cXnMLp/NBaLFmzsLRSMRERE2lAbDPP6x4d56j8fcGZoB4kOG55x5/K988YS47Z3dXnSyRSMREREWnG00s8jK3N5cX0eFtPBWLeL9H5JXLdgGNEKRb2SgpGIiMgXhMImG/eXcd+ydWwuCgEwe0R/rp93FiPStflrb6ZgJCIi8jlVgSAvfHiAVatWMd4ooNoxhIvnTuXqs7OIcOpjs7fT37CIiAj1+5ztLa7iN6/nsPLTQibZwhh2+PrYKK6cORirtvXoExSMRESkz/PXhVj1aSH3vraD/IoABjB0wlQuGOZkyriRXV2enEYKRiIi0qcVev08tWonezatZRgh/BEj+fF5I7lwXCpuh7Wry5PTTMFIRET6pNpgmG355fz6tU/Zn1/ARc5SLIbJdRdlMW1culpnfZSCkYiI9DnlNbX8c/MhHn1zFxW+Ohy2SNyDz+DCM4YydsSQri5PupCCkYiI9BmhsMm+4ip+99+P8e7aQDCYwcDEOH5+/kimD03EZVfrrK9TMBIRkT6hKhDk/T3F3Pvapwyp3MpAWwVp0Xauv2Y+AxMisah1JigYiYhIL2eaJocrfLzwYR6/X7uX2mCYWvdAhsQWcNVXvsygpKiuLlG6EQUjERHptfx1IbYXVPC71zazP/8wteE4JmbE8tPzRzAuPQaXXR+D0pR+IkREpFcqqvTz1qdFPLN8E+eEPibTAbZRg7l+wXjSY93a1kNapGDUDtnZ2WRnZxMKhbq6FBEROY7aYJgDJdX8Yc0+/r4xj7BpY4wnmqwED/8zezhpcZ6uLlG6McM0TbOri+gpvF4vMTExVFRUEB0d3dXliIjIF5RV17I5r4zHX9vI5qNhTAzmj0zm/83IZFRGglpnfVRHPr/1EyIiIj1eMBSmoNzPq1sLePOdNYwzDmJxpjN39iy+PDGN1BiXWmfSLgpGIiLSo1X669hVWEX227t5a2cRQ6wWLA6YN9DDFWdmEhvh6OoSpQdRMBIRkR4pHDY54vXz4Z4Sli7fQb63DosBUyZOYO6gMzhj7DC1zqTD9BMjIiI9jq82xIHSal76cD85m9YyyaimNmI8SxaNYOawJPqrdSYnSMFIRER6DNM0OVoZYOeRSpauzCUnr4jFrjJcRpDbZ8Yza2x/Ytz2ri5TejAFIxER6RECwRD5ZT7eyTnKo2/m4vUHcdhcxIw8h2mDE5g6YRROm/Y6k5OjYCQiIt1eaXUt+4urefbdHLy563AEUxiYmMIPFw5nQmasWmfSaRSMRESk2wqGwhwq97H9kJcHlu+kn/dTRtrKyPDUcfGl8xmcEq3WmXQqBSMREemWvP468ktreG3bkcbNX6vcWUyMtzFn7jzGpMfhsFm6ukzpZRSMRESkWwmHTQ57/RworuapFR9TeGg/taFkJmbE8v35wxjabw79otU6k1NDwUhERLqNmtogeaU+Nh4o4/EVHzM7tJnBjhDTBmfylTmjyYyPUOtMTikFIxER6XKmaVJUGeBIhZ+/fnSQv23IwwQKI5IZERNiwVkjGJ4SrdaZnHIKRiIi0qUCwRB5pT72FVfz5Bsb2XY0iImV+SOTuWHamWQmuEmNi1DrTE4LBSMREekyJVUBDlf4WZ1zlNff+YApxj6inQmcOXsRs4cnkx7vJtql1pmcPgpGIiJy2tWFwhwq81Ho9fPMu3t5a2cRKRY7FqfJ5LRI5o1IYmBSpFpnctopGImIyGlV4avjUJmPnYe9LF2+nXxvEIsBcyaPYlbWBIYPzqR/jFutM+kSCkYiInJahMMmBRU+SqpqWbYxj082vs80awlrIyZy66LRjEuPVetMupyCkYiInHLVgSD5ZT6OVPh55M1cPs4r4SJnORFGHd+b4mHywHgy4jxqnUmXUzASEZFTxjRNCr0BiqsCrNtX+rnNX+2kTpjNuEQrE8aNISXaqdaZdAsKRiIickr460Lkl9VQURPk2bW7KM9ZR0I4hsTEDG5bNJyshAi1zqTbUTASEZFOV1xVv1jjgZIaHly+k8iKvZxhL2GQxcsFixeSEBNBZrwHu1WtM+leFIxERKTT1IXC5Jf5qPTV8d/tR/jD2n3UBsPEutOZlWxjyhlnkJkUo9aZdFsKRiIi0ikqauo4VO6jvKaWJ1Zup/JQLrXB/kzMiOP784eRGOUkI95NlFpn0o0pGImIyEkJhU0Kyn2U19Tx8aEKHl3xKbODG4mw1zFpYDKLF44m0mVT60x6BAUjERE5YVWBIPllNfhrw/zfus82fz0YmcHEiHKmTx1HvxgXyVFqnUnPoGAkIiIdZpomR7x+iitrOeL1k/3GJnYV+zBxMn9kMt+YfhYeh0FWUpRaZ9KjKBiJiEiH+OtC5JXW4K8L807uUZatXs9Zlt2kOyMYOfNCZg5LIcJpJUOtM+mBFIxERKTdiir9FHkDVAeCjZu/RhpODJfBkORozhoQQ3K0U60z6bEUjERE5Lhqg2HyymqoCYTYVVjJb5d/wgFvCIsBF04ZwoIh40lMSiQzIYJIpz5apOfST6+IiLSptLqWwxU+giGTVzbms3Xjh8ywHsYSMY6bFk1kdGqMWmfSaygYiYhIi4KhMIfKfXh9QUqqAix9M5dt+eUscFRiN8JcN8rG6NT6xRqTo11dXa5Ip1AwEhGRZip8dRwq8xEKm3ywt4TH3sqlMhDCabMy/My5jIz0MWj4KDLiPWqdSa+in2YREWkUCpscrvBRVl2Hvy7EH9/dTfnuDQwy7VQnDeO2hcNJi3OrdSa9loKRiIgAUB0Ikl/mozYYZu/RKh5ckYO1ooC5zqOYGMw/dxGxsW6So9Q6k95LwUhEpI8zTZNCb4CjlQHCpsm/txbw3Pv7CYZN4j0pxGQ4GTNyOAnxsWTGe4hQ60x6Mf10i4j0YZ9frLGsupbfrfgEozAHM5zG1IGJfGfuUGLcdiJdNjLi3NjUOpNeTsFIRKSPOloZoNDrxzRh/f5SfvtWLrPC20iw1zA+I4YvnT8Di8VoWLBRrTPpGxSMRET6mM8v1hgIhnj2vf385+PDAByKHUSaPY9pU6fgsFvIiFPrTPoW/bSLiPQhZdW1FFT4CIfhQEk1j72xlaMVVYCHL49P5ZppWVgNkxiPk3S1zqQPUjASEekDPr9Yo2mavPbxYV59fxuzbbsIumyMmP0VzhicgmFASrSLpChnV5cs0iUUjEREejmvv4780vrFGit8dTz6Zi4bDpRhx4XhtNM/PoYx/SJw2CxkxLvxOPTRIH2XfvpFRHqpcNikoGGxRoBNB8t4cuUnHPEZ2K0G100bxpyBE/BERhMb4SA9zoPVYnRx1SJdS8FIRKQX+vxijXWhMH/5YD+5H29mgT2fT2JGc/15Z5OVGIFhQL8YF4mRap2JgIKRiEiv8vnFGgHySmt4aEUOe4urmWoPYDNMLhoQJiuxvnWWGe/B7bB2cdUi3YeCkYhIL/H5xRpN0+S/24/wh7V7qQ2aRLtsLJg9n/6UkjF4OLEeO6mxbrXORL5AwUhEpBf4/GKNXl8dj63KIZj3MVONIJUZE/n+/GHERzgwjGRSY93ERzi6umSRbknBSESkB/v8Yo0AW/PLWboyF6OmjAudhVgMmHlWAvERDpz2+taZy67WmUhrFIxERHqozy/WWBcK88JHB3llUz4mkBabSPqQqWT0SyIxpT+xHjtpsW4sap2JtEnBSESkh/n8Yo0Ah8p8PLJ8O3EVOThJZdboDG6cPhCX3YphQFqsmzi1zkTaRcFIRKQH8frrOFTmIxgyMU2TNz8t5Jk1eznHyCXTVs6EFAcXzJkDgMtuIUOtM5EO6ZOb4Fx88cXExcVx6aWXdnUpIiLtEg6b5JfVcKC4hmDIpMof5IHlOfxu1W78dWEq44bjjorlrLPPASAuws7gpEiFIpEO6pMzRrfeeivXX389zz33XFeXIiJyXJ9frBFge0EFjy3/hLCvAqslhiunDuDiiWlYjLOwWAzS49zEetQ6EzkRfTIYzZkzh9WrV3d1GSIibfriYo3BUJgX1+exfFMu5zlysDpNRs/5CmMGpQFqnYl0hm7XSnv33Xe56KKLSE1NxTAMli1b1mzME088wcCBA3G5XEyePJk1a9ac/kJFRE4hf12I3UVVjaHoSIWfn7zyMS9tyKMi7MJwRREfF0dWggeA+EiHWmcinaDbzRhVV1czfvx4rrvuOi655JJm33/ppZf43ve+xxNPPME555zD008/zXnnnceOHTvIzMwEYPLkyQQCgWaPXbFiBampqaf8NYiInIzPL9YI8HZOEX9ZvYPiOisRDhu3zBnCGemTsTsc2O020mM9xHjsXVu0SC/R7YLReeedx3nnndfq95cuXcoNN9zAjTfeCMCjjz7K8uXLefLJJ7nvvvsA2LhxY6fUEggEmgQsr9fbKecVEWlJbTBMflkN1Q2LNVYHgjz1zh7y93zKefaD5EcN5soL55Ec7QLA7ahvnTltmiUS6SzdrpXWltraWjZu3MjChQubHF+4cCHvv/9+pz/ffffdR0xMTOOvjIyMTn8OERGoX6xxV1FlYyjaedjLrS9uZnXuURxGGJsRZmpCHUlRTgASGlpnCkUinavbzRi1pbi4mFAoREpKSpPjKSkpHDlypN3nWbRoEZs2baK6upr09HT++c9/csYZZzQb99Of/pQlS5Y0fu31ehWORKRTfXGxxlDY5O8b83hx3QFCpkFylJNrF8wjKlBIWtZQrFaD9DgPMW61zkROhR4VjI4xjKZL2pum2exYW5YvX96ucU6nE6fT2aHaRETa6/OLNQIUef08vCIHe3EOC+1efAPO4ebZQ4lw2oAY3A4rmfEeHLYeNdkv0qP0qGCUmJiI1WptNjtUVFTUbBZJRKS7CodNCip8lFXXNR5bs+so2W/vhjofi52FOIwQU4fZGkIRJEY56Bft6tB/AkWk43pUMHI4HEyePJmVK1dy8cUXNx5fuXIlX/7yl7uwMhGR9vniYo2+2hDPrNnDm58WATA8JYExo+YS7bCQNnAoVotBerybaJdaZyKnQ7cLRlVVVezevbvx63379rFlyxbi4+PJzMxkyZIlXHXVVUyZMoWzzz6bZ555hoMHD3LzzTd3YdUiIm374mKNALmFlSxdvoMM324SLEnMnzyc/5mSgc1a3yrzOK1kxKl1JnI6dbtgtGHDBuY0bIAINF78fM011/Dss89y+eWXU1JSwi9/+UsOHz7MmDFjeP311xkwYEBXlSwi0iZ/XYi80hr8dfWzRKGwySub83nho4NMsR5gpO0o42PruOCM+RiW+hCUFOUkJdqp1pnIaWaY5rElxDomLy+vz92h5fV6iYmJoaKigujo6K4uR0R6gKJKP0XeQONijcVVAR5Zmcu2QxUAzBwYxYTaTxh/5gyS0zKxWgwy4t1EqXUm0mk68vl9wjNGAwYMIC4ujvHjxzN+/HgmTJjA+PHjCQQCZGdn85e//OVET93tZGdnk52dTSgU6upSRKSHCARD5Jf5qAl89r7xwZ5inl71KVHBMlz2RG6aMZh5I5OBcRiGQYTTSka8B7tVrTORrnLCM0b79+9ny5YtbNmyhc2bN7Np0yYKCgoAiI6OpqysrFML7Q40YyQi7VFaXUtBua9xlshfF+L3a/by7o58vuTagceoY/SsLzFiyKDGxyRHO0lpWNFaRDrXaZkxysrKIisri8WLFzce++CDD7jmmmu4//77T/S0IiI9Vl0ozKEyH5X+YOOx3UVVPLQih0PlPgzsOGL7EWlW0S8uEgCb1SAj3kOks9td8inSJ53wjFFr3njjDW6//fZO26+sO9GMkYi0pqKmjkPlPkLh+rfUsGnyz82H+OeHuVSFbcRGuFiyYBijUjyAgc1uJ9JlIyPO3XgXmoicGqdlxqiurg67vfnFgUOHDmX79u0neloRkR4lFDYpKPdRXvPZYo3FVQEeeTOX8oL9XOjYT3VEKl+9+EuNF1QbRn3rLDlKrTOR7uaEg1FERASjRo1i4sSJTJgwgYkTJ5Kamspjjz3WbJNXEZHeqNJfP0tUF/xs4v39PcU8tmo3VYEgWXYrDiNEv8ggHnv9bfc2q0FmvKdxRWsR6V5OuJW2du1atm7dytatW9myZQvbt2/H5/MB9bvdT548mXHjxjFu3DhGjhzZqUV3FbXSRATqt/Q44vVTUlXbeOzYBdZv7jhMGAtDkiO5bcFwrNWFJKdmYrFYiHLZSFfrTOS068jnd6ddYxQOh8nJyWm8U+1YaCoqKuo1t7krGIlITW39lh6BhsUaAXYVVvLwihxiq/cz3HoUy4h5fG3akMbb7g0DUqJdJEVpU2qRrnBarjH6IovFwsiRIxk5ciRXXHFF4/HCwsLOegoRkS5jmiZFlfVbehz772TYNHll0yH+96MDGOEg57iPEkGAsXFVjaHIbqtvnXkcap2J9ASn/F+qdr0XkZ7OXxciv6wGX+1ns0RfXMF62uBk5owdRG1lKQNHjAMg2m0jPc6D1aJtPUR6Cv0Xph208rVI33W0MkCh18/nLzp4b3cx2W/nMjx0gIH2aC6cMZkFI1Ma9jXLwDCgX4yLxEi1zkR6mk5fx6g30zVGIn1HbTBMflkN1Z/b0sNXG+L3a/eyckchY2xHOMOej83h4rzLr8PuqA9BDpuFzHgPboe1q0oXkS/okmuMRER6i7LqWgoqfIQ/65yxq7CSh1bkUFDhxwBGjJlIotdgyKjxjaEo1mMnNdat1plID9ahYLRkyZJ2j126dGmHixER6UrBUJhD5T68vs+29AiF61ewfumjvQwwiknwpLFk4XDGpcdimoMwDAPDgNRYN/ERji6sXkQ6Q4eC0ebNm5t8vXHjRkKhEMOHDwcgNzcXq9XK5MmTO69CEZHToMJXR0G5j2Dos6sLiqsCLF2Zy/ZDZSx2bifGEmD0WUMZnh4LgGEYOO31rTOXXa0zkd6gQ8Ho7bffbvz90qVLiYqK4rnnniMuLg6AsrIyrrvuOmbMmNG5VYqInCItbekB9RdYP/52/QrWLruNpAHDsJXtJzEhoXFMrMdOWqwbi1pnIr3GCV98nZaWxooVKxg9enST45988gkLFy6koKCgUwrsTnTxtUjvUh0IkldW02RLj2MXWK/dkYeJQXpyHD9cOJz+0U6CwTrsDieGAWmxbuLUOhPpEU7Lxdder5fCwsJmwaioqIjKysoTPa2IyClnmvVbehRX1jY5fuwCa7OyiMWuvdgi41n8lZk4bPVtMrvDictuIUOtM5Fe64SD0cUXX8x1113Hww8/zFlnnQXAhx9+yA9/+EO+8pWvdFqBIiKdyVdbv1ij/3NbeoTCJq9szueFjw4SCpsM8HhwGybRThMzWAs2NwDxkQ76R7vUOhPpxU44GD311FPcdtttXHnlldTV1ffmbTYbN9xwAw8++GCnFSgi0hlM0+RoZYCiz23pAZ9dYL3jUBkhLJwzOIFb5gyhtmIYsYnJWK02LBZIj/UQ47F33QsQkdPipBd4rK6uZs+ePZimyZAhQ4iIiOis2rodXWMk0jMFgiHySn34apuuXl9/gfUuUoNHmGQvIHHSQhZOHNKwgnU9t6O+dea0qXUm0lOd1gUeIyIiGDdu3MmeplvTliAiPVdJVYDDFU239Pj8CtYGJmMiy3GH6uhfW4BhDG0clxDpoH+Mq0lQEpHe7aRmjNasWcPTTz/Nnj17ePnll0lLS+P5559n4MCBTJ8+vTPr7BY0YyTSc9SFwuSX+ajyB5sc/+IK1pdOTmfxqDgK8/YwZPREDMOob53FeYhxq3Um0ht05PPbcqJP8o9//INFixbhdrvZvHkzgUAAgMrKSu69994TPa2IyEkrr6klt7CySSgKhU3+vjGPH/1jK8nVe5niKeHXi8dw9dlZRMfEMHTMJAzDwO2wMjQ5SqFIpI864WD0q1/9iqeeeorf//732O2fvYFMmzaNTZs2dUpxIiIdEQyFOVhSQ15p033OiqsC3PGvT/jLBwdIo5SJ9gLGGQcYHNP0LTApysngpAgcthN+axSRHu6ErzHKyclh5syZzY5HR0dTXl5+MjWJiHRYpb+O/LKmW3rAF1ewtvDl6WcSW+wkJW0Anqj6KXWrxSAj3k2US7NEIn3dCQej/v37s3v3brKyspocX7t2LYMGDTrZukRE2iUcNjns9VNa1XSxRl9tiN+v2cuqTwsYZSvCnzSY2xaNJDXWDfRrHBfhtJIR78Fu1SyRiJxEMLrpppv47ne/y5/+9CcMw6CgoIAPPviA2267jTvvvLMzaxQRaVFNbZC8Uh+1wXCT47mFlTy8IoeCCh/nO3JJsVYzdFD/hlD0meRoJ8lRTt11JiKNTjgY/ehHP6KiooI5c+bg9/uZOXMmTqeT2267jW9/+9udWaOISBOmaVLoDVBc1XSxxi+uYJ0Y6WT8mCmU5a4nJTWzcZzNapAR7yHSedIrlohIL3PCt+sfPHiQ9PR0/H4/O3bsIBwOM2rUKCIiIsjLyyMzM/P4J+lhdLu+SNfz19Vv6eGrbTpLdLQywCNv5pJ7qBinEWLsoDRumTOEKJedutpa7I76DV8jXTYy4tzY1DoT6TNOywKPAwcO5PDhwyQnJzNlypTG4yUlJQwcOFCLIYpIpztaGaDQ23SxRvjsAmtnbQWLXbuJ9Li5YP7Mxjtm7Q4HhnGsdebqgspFpKc44WDU2kRTVVUVLpfeeESk89QGw+SV1VATaPofrmMXWK/8tBCAjMQ4YkJ2XA4rtT4fdnv9LJHdZpAR5yFCrTMROY4Ov0ssWbIEAMMwuPPOO/F4PI3fC4VCfPTRR0yYMKHTChSRvq20upbDFU3XJYL6C6wfWpHD0YpqDKxcOjmdr52ZSXXFICKiYrA1zBZFuWykq3UmIu3U4WC0efNmoH7G6OOPP8bR0LcHcDgcjB8/nttuu63zKhSRPikYCnOo3IfX13RLj1DY5JVN+byw7iCZRjGXu/MYeOYCpo7NAiAmPhEAw4CUaBdJUc7TXbqI9GAdDkZvv/02ANdddx2//e1v+8RFyNpEVuT0qvDVcajMRyjctGV/tDLA0pU5fFLgBWBiQi2OmiAc3Q0MbxznsFnIiHfjcah1JiIdc1J3pWVkZLS4/sfBgwd1V5qIdFgobHK4wkdZdV2z731xBeubZgxm1pBY9udsZ/DoCVgs9a2yGLedtDg3VovWJhKReqf9rrTP011pInIiqgNB8suaL9b42QXWRxhtKyQt2uSSL13YuFjj0LGTgPrWWf8YFwmRap2JyIk7qbvSWpot0l1pItIRpmlyxOunuLK22fdyjlTy8MocDlf4STKqOdOeD3XgDJQBn61i7bRbyIjz4HZYT2PlItIbndRdaXfccYfuShORE+avC5FXWoO/ruksUShs8vLGPP667iBhExIjnXx/wVisR2JwRUQQn9y/cWysx05arBuLWmci0gl0V5qIdImiSj9F3kCzxRqLvH4eXpnLzsPljLUdIXbASG6eM5JIlw3Szm4cZxiQGusmPsKBiEhn0V1pInJaBYIh8st8zRZrBFidU8ST7+yhpjbEPOd+Mi2lpDkiiHSNbTLOabeQGe/BZVfrTEQ61wlfY/TnP/+5M+sQkT6gtcUaqwNBnnpnD6tzjwIwol8UF0yeTe4H/yVjyIgmY+Mi7KTGqHUmIqdGh4LRkiVLuOeee4iIiGi81qg1S5cuPanCRKT3aG2xRoDtBRUsXZlLWWU1yRY/86eM4qtTMrBaDAZlXI/VVv82ZRiQHucm1qPWmYicOh0KRps3b6aurq7x961p6W41EembWlusMRgK8+KGPP6+IY8I/HzFvYsoOywcPb1xDaJjocjtsJAep9aZiJx6HQpGb7/9Nnv37iUmJqbxWiMRkZaEwiYF5T7Ka5ov1lhQ7mPpylxyCisBOGNYGv2qCwnWBgj4fbgjIhvHJkQ66B/j0n+4ROS06PA1RkOHDm2ysOPll1/O7373O1JSUjq9OBHpmaoDQfLKaqgLNp0lMk2Ttz4t4uk1ewjX1RLhcHDLnKHMGJpETWUadqcTu6N+gUarxSA93k20y94VL0FE+qgObzf9xR1EXn/9daqrqzutIBHpuUyzfkuPvUerm4WiSn8d9y/P4berdpEUKuWrnu38/CwPM4YmAeCJim4MRRFOK0NTIhWKROS00w6LItIpWlusEWBbfjmPvJlLcVUtVovB3CwnlsN1lB7chTl2fGObzDAgOcpJcrRWzxeRrtHhYGQYRrNev3r/In1ba4s11oXCvPDRAV7ZdAgTk9QYN7ctHM6QpAj27kwma/joxvcPu80gI85DhFP/XxORrtPhdyDTNLn22mtxOuunvP1+PzfffDMRERFNxr3yyiudU6GIdFttLdaYV1bDwyty2HO0iuHWYibG+vnKJZfhdtS/7QweNb5xbLTbRlqsG5u1w919EZFO1eFgdM011zT5+sorr+y0Yrqr7OxssrOzCYWav/mL9FWtLdZomib/3X6EP6zdR20wTLIzzDRbPtSEKM7bQ8bg4Y1jDQP6x7hIiHSe5upFRFpmmF+8mlpa5fV6iYmJoaKiQluhSJ/V1mKNFb46Hlu1i4/2lQIwISOW780bSmXBbuoCfoaMmdTYOtO2HiJyunTk81vNfBFpt9YWawTYdKCMR9/Kpbymlon2I0wcP5YvTx2OxTBIGDa6ydhYj520WG3rISLdj4KRiBxXW4s11gbDPPfBfv69tQCAuVFHGBA8RExhHZjD6vtlDSwWSIvVth4i0n0pGIlIm1pbrBHgQEk1D63IYX9JDQAXju3P5RPG8uF//8HQMZOwWD67mNrtsJIR78ZpU+tMRLovBSMRaZFpmhzx+imurG3xe//Zdpg/v78PMxRkqNvPFfPO4IyseAAWXnYNFstnASgxykG/aG3rISLdn4KRiDTT1mKNZdW1PPrWLjYdLMNJkK9E7sJt+hgSObFxzLFQZLUYZMS7idIK1iLSQygYiUgTrS3WCLBuXwm/fWsXXn8Qh9XCtdOGkni0ktKjRwgFm15/FOmykR7nxq61iUSkB1EwEhGg7cUa/XUh/vTePt745AhO6hgYH8UPFo1kQEIEtYEETNPE6XIDDdt6RDtJjtK2HiLS8ygYiQil1bUUlPtanCXac7SKh1bkkF/mo5/FyyLPAYYNGcOAhPrV7h3OzwKQ3WaQGe/B49Bbi4j0TJrjFunDgqEw+4urOVTWPBSFTZNXNuVz29+3kl/mI97j4Joz+mMJBSjK208o2HSBxxi3naHJUQpFItKj6R1MpI9qa7HGkqoAS9/MZVt+BWBy1qAEvj1nKDFuOwfjXKQOGILVVv/2oW09RKQ3UTAS6WPaWqwR4L3dxTz+9m6qAkGG20uZHlPOBfOnYnfU31mWOWRk41iX3UKGtvUQkV5EwUikD6kKBMlvZbFGX22I36/dy8odhQAMS3QxK1RIXXU1ez/dyvDxZzQZHxdhJzVG23qISO+iYCTSB7S1WCNAbmElD63I4XCFHwO4dHI6V5yZSXlRCkcP5zN07OTGsRYLpMd6iPFobSIR6X0UjER6ubYWawyFTV7elM9fPzpA2DQ501PCwikjmDouC4Ck/hkk9c9oHO92WMmM9+Cw6b4NEemdFIxEerG2Fmss8vpZ+mYu2wu8AFzYr5qkiv2UbC+mbsRA7I6mF1MnRTlJiXZqWw8R6dUUjER6odpgmLyymhYXawR4J/coT67eTXVtCLfdys2zBjNjUCzvvl7CoBHjsNkdjWNtVoP0OG3rISJ9g4JRO2RnZ5OdnU0o1PKHjEh3UlZdS0GFj3DzzhnVgSBPvbuH1TlHsRBmWkKA686fQb+Y+kUa537pCgzLZ22ySJeNjDg3Nm3rISJ9hGGaLU2yS0u8Xi8xMTFUVFQQHR3d1eWINBEMhSko91Pha/k2/B2HvTy8IoeiygA2I8zX4/Zi8ZUzdd6FpGUNaTLWMCAl2kVSlNYmEpGeryOf35oxEukFKv115Jf5CIaa/z8nFDZ5cf1B/rYhj7AJKdFOfrBgOKF8C/tzPsFqbboGkcNmISPerRWsRaRP0jufSA8WDtffhl9S1fJt+IcrfDy8IpecwkrsBJk7NIlvzBmOx2EjnHI2g0dPxO2JaBwf67GTGuvGqrWJRKSPUjAS6aF8tSHyymoItHAbPsDqnCKeWL0HX12IdIePRZ799LNV4baPAsBisTaGIsOA1Fg38RGOFs8lItJXKBiJ9EBt3YZfUxvk6Xf2siqnCIBR/aO5acoAtq76lPLiIgL+Glzuz2aJtK2HiMhnFIxEepBAMER+ma/V2/B3F1XxwPKdHK7wYzVMLj9jAF+dkoHVYuCedxGJ/VKbrE8UH+mgf7RL23qIiDRQMBLpIdq6DT9smvxryyH+8sEBgmGT0RFVnOMuYN7oCY3XC/XPHNg43mKB9DgPMW6tTSQi8nkKRiLdXDAU5lC5D68v2OL3y2pqefTNXWw6WAbA2QPjObP2IN5SL7lb1zNh2twm4z1OKxlx2tZDRKQlCkYi3ZjXX8ehVm7DB9h0sIxH3sylvKYOh9XCjTMGcu7oflR7+7M/dzsjJ53VZHxytJPkKG3rISLSGgUjkW4oHDY57PVT2spt+HWhMM9/eIB/bj4EmJwdXcG5Y9OYNKY/AJExcYw5Y3rjeJvVICPeQ6RT/+RFRNqid0mRbqamNkh+ma/V2/ALyn08uCKH3UVVAFw8EGKP7CZv236GDxlERFRMk/FRLhvp2tZDRKRdFIxEugnTNDlaGaCosuXb8AFW7SziqXfq1yaKctr4zryhnDUwnvdXlJCcmokn8rOl7g3jWOvMdZpegYhIz6dgJNINBIIh8kp9+Gpbvg2/pjbIk+/Ub/5qYDI7oZqrL5hFUrQbgGkLv9zkuiGb1SAz3kOEWmciIh2id02RLlZaXUtBua/VWaJdhZU8uCKHwxV+LIbJVYl5WKqKKN2XQNL4MwCahKJIl40Mtc5ERE6IgpFIFznebfhh02TZ5kP85cMDhMImSVFObls4HE9lPNs+fKdJ2+yY5GgnKdFqnYmInCgFI5Eu4PXXkV/qIxRueZqorLqWpW/msiWvHBshZmVFc/P8sUS6bJj9RtEvI6vJth5Wi0FGvJsolxZsFBE5GQpGIqdROGxSUOGjrLqu1TEbD5Tx6Ju5lPvqSLQF+FLUAaKDTtz2sUB92+zzocjjtJIZ78Gu1pmIyElTMBI5TWpqg+SV+qgNtnwbfl0ozF8+2M+yLQUAZCV4+O7M4ex8excBX4iaSi9RsfFNHpMY5aBftEsLNoqIdBIFI5FTzDRNiioDHG3jNvxDZT4eXLGTPUersRDm/LFpXHfOQBw2C3ELvkRkTBxOl7txvPY6ExE5NRSMRE6h492Gb5omb+cU8eQ7e/DXhRnsrGaO+yAzRw1v3MssISW1yWPcDguZ8RHa60xE5BTQO6vIKVJSFWBXYVWbaxM9vDKXR97chb8uzNi0GC4ZUEsoUM3OLR+1+Jj4SAeDkyIVikREThHNGIl0srpQmENlPir9Ld+GD5BbWMmDy3M44vVjMeBrUwdw6aR0QnVDyd0Wx4iJU5uMNwxIj3MT63Gc6vJFRPo0BSORTlThq+NQWeu34YdNk1c2HeJ/P6pfm2hCRAULBkcyc0oGAFanq8nmrwAuu4WMeA8uu/WU1y8i0tcpGLVDdnY22dnZhEItt0RE2nMbfml1LY80rE0EMDfTzoCjuyjeBSXDhza7lggg1mMnLdaNxaK7zkRETgfDNFu7T0a+yOv1EhMTQ0VFBdHRzVcdlr6pOhAkv6z12/ABNuwv5ZE3c/H6gzhsFm6aOYgFI1PY+sFqnC43wyecicXy2XVDhgGpsW7iI9Q6ExE5WR35/NaMkcgJas9t+HWhMM++v59/by0ATM6J8fI/i6aTlRwDwPizZzdbg8hpt5Cp1pmISJdQMBI5Af66EPllNfhqW58lyi+r4cHlOewtrgbgiuQiXJV5lOy0k5W8EKBZKIpx20mLc2NV60xEpEsoGIl0UElVgMMV/lZniUzT5K1Pi3jq3T0EgmGiXDa+N28oA11ZfLDyCPHJ/TFNs0koMgzoF+MiMdJ5ml6FiIi0RMFIpJ3qQmHyy3xUtXEbfnUgyBOrd/PurmIshDmjn4Nbzp1IQkPgOffyG3A4XU0eY7cZZMZ78Dj0z1FEpKvpnVikHY53Gz7AziNeHlyeQ1FlgEijlkvjDuKuqyPSNr5xzBdDUZTLRka8R60zEZFuQsFIpA2hsElBuY/ymtZvww+bJv/YmM//fnSAsAnJUU5+MG8khz7MI+APUVVR1mSfM6hvnSVHO0mOcrVyVhER6QoKRiKtaM9t+CVVAZa+mcu2/AqshJkxNJlbZg8hwmkjff5F2O0O3BGRTR5js9a3ziKc+ucnItLd6J1Z5AtM0+SI109xZW2b49btK+XRt3Kp9AdJs1ezKOIgZwzt1xh4omPjmz0mwmklM96Dzaq9zkREuiMFI5HP8dWGyCurIVDX+ixRXSjMn9/bx6vbDgMwKDGC/0kPcjinmtxtG0gbOLTZbfhQ3zpLiVbrTESkO1MwEqF9izUC5DWsTbSvYW2iL41P5dppWVgNkxyPiyFjJjYLRVaLQUa8myiX/VS+BBER6QQKRtLntWexRtM0WflpIc+8u5dAMMxwl5cFqWEWTj+nMQiNnHRWs8d5GlpndrXORER6BAUj6dOKKv0UedueJapqWJtoza5iAKb0dzLOu5vqw2Hy9+aQMXhEi49LjHLQL9rVYltNRES6JwUj6ZMCwRB5pT58taE2x3162MtDK+rXJrIYcOVZA7hkUjp7t1vxVVeRljW02WMsFkiP8xDjVutMRKSnUTCSPqe4KsCRNrb0gPr1i17elM9fPzpA2DSZElnOJbOmMGZgfwCGjJnU4uPcDgsZ8R6cNm0AKyLSEykYSZ9RGwyTX1ZDdaDtWaKjlQEeeTOXjw9VALA4uZy4yj2UbPdjDrgEw9Ly9ULxkQ5SY9Q6ExHpyRSMpE8ora7lcIWPcOvXVwOwZtdRslfvpjoQwmW3cNPMwUxNdfDOq4dIzRpcv2T1FxgGpMe5ifU4TlH1IiJyuigYSa9WFwpzqMxHZRsbvwLU1AZ56p09vJ1zFAOTSYkmN507mdTY+q08Fn31euyO5sHHZa9vnbnsap2JiPQGCkbSa5XX1FJQ7m9z41eov8D64ZU5FHoDuIwgX407iMPvJdIcDdQHo5ZCUazHTlqsG4s2gBUR6TUUjKTXCYbCFJT7qfC1vvHrsXEvbsjj7xvyGjd//f78MZRvK6X0aBU1VV6i4xKaPc4wIDXWTXyEWmciIr2NgpH0KhW+Og6V+Y47S1RQ7mPpylxyCiuxEWLmsBRunlW/+as/bhGhUJCIqJhmj3PYLAxIUOtMRKS3UjCSXiEUNiko91Fe0/YskWmavPlpIc+s2Yu/Lkyaw895kQcZnuxu3PzV5Ylo8bExbjtpcW6sap2JiPRaCkbS41X668gv8xEMtT1L5PXV8fjbu/lgbwkAY1Kj+drQKHat+4T9OR8zdMwkrLbm/yQMA/rFuEiMdJ6S+kVEpPtQMJIeKxw2KajwUVbd9iwRwJa8ch55M5fS6lqsFoOvT83kKxPTsRjgNsJkDBnRYiiy2wwy4z14HPqnIiLSF+jdXnqk6kCQ/DIftcG2FyaqC4X5ywf7WbalAICx0X7mxJUzd8LUxpbYkDETW3xslMtGepwbmzaAFRHpMxSMpEcJh02OeP2UVNUed+yBkmoeWpHD/pIaAM4flUjG4XeoLPKx6+NNjJhwZouPMwxIiXaRFKXWmYhIX6NgJD1GTW39LFGgru1ZItM0+c+2wzz7/n5qQ2GiXTZunTeUqQMTOHzQwZG8fa3OEql1JiLSt+ndX7o90zQp9AYorgq0ufErQFl1LY++tYtNB8sAmJfs4+KzRjAgs349ov6Zg+ifOajFx0a7baTHeXTXmYhIH6ZgJN2avy5EXmkN/uPMEgGs21fCb9/ahdcfxG41uGZoiNCB7ez8MJ/Ufl9vcfVq0F1nIiLyGQUj6ZZM0+RoZYCiyuPPEvnrQvxx7T7+u/0IAFkJHm5bOJz+kVbeLt1D5tBR2Fq44wzqF2zMjPfgdmjBRhERUTCSbshfFyK/zIevNnTcsbuLqnhoRQ6Hyn2AyaXDXHxt3gTsDXeSzf/KVS3ehg9asFFERJpTMJJu5WhlgEKv/7izRKGwySub83nho4OEwiYJHhuXxx/El1dA6eEkUtKzAFpdsLF/jIsEtc5EROQLFIykWwgE62eJagLHnyUqqvTzyMpcPinwAjBtcAK3zB7C3s01HCgvIuD3t/pYp72+daa9zkREpCUKRu2QnZ1NdnY2odDxP7Sl40qqAhyuOP4sEcC7uUd5YvVuqmtDeOxww7QsFoxJwzAMxp45k8GjJhAVG9/iY2M9dtJi3VjUOhMRkVYYptmejyMB8Hq9xMTEUFFRQXR0dFeX0+PVBsMcKvdR5Q8ed2x1IMhT7+5hdc5RAMYnWplu201iUjJTZi1q87GGAamxbuIjWr4rTUREereOfH5rxki6RFl1LQUVPsLHvwuf7QUVLF2ZS1FlAIsBX52SwfwMC+/9dx1HAjX4aqpxeyJafKxaZyIi0hEKRnJaBUP1s0Re3/FniYKhMC+uz+PvG/MIm5AS5eAHC0cwsn992p8ycxFJqRmthqK4CDupMWqdiYhI+ykYyWlTUVPHoXIfofDxu7cF5T4eXplDbmEVAOdl2Rke2sOg2DGNYzKHjGjxsYYB6XFuYj1qnYmISMdo23A55YKhMHmlNRwsrTluKDJNkxU7jvDdlzaTW1hFhNPKDxcOY3jdLiqKC9mx6YM2H++yWxiSHKlQJCIiJ0QzRnJKef11HCrzEQwdf5bI66vj8bd388HeEgDGpsXw/fnDSIpyUpF4Lrs+2cSYM6a3+vj4SAf9o11qnYmIyAlTMJJTIhQ2OVzho6y6rl3jNx8s49E3d1FaU4vNYnDlCBtnZrlIiqpfhDEmPpEpMxe2+FiLBdJjPcR47J1Wv4iI9E0KRtLpqgJB8stqqAsef5aoNhjmLx/s519bCwBIi3XzzXEu9q9fyeZ8BwlJKXiiWr+10u2wkBHvwWnTXWciInLyFIyk04TDJoe9fkqrats1/kBJNQ+tyGF/SQ0A543px/XnDMRhNag8uJ2E5P64WrnjDCAh0kH/GBeGodaZiIh0DgUj6RQdmSUKmyb/2VbAs+/vpy5kEuO28Y1xHmZOGdwYcmacdwkWa8uzQBYLpMd5iHGrdSYiIp1LwUhOSihscqQDs0Sl1bX89q1cNh0sB2BKZizz3Psp2rabvREmg0eNB2g1FLkdVjLjPThsuqFSREQ6n4KRnLBKf/26RO2ZJQL4cG8Jj63ahdcfxGG1cP05WZw/tj97ttdxNH8v0PZ5EqMc9ItW60xERE4dBSPpsI7eceavC/GHtftYvv0IAIMS3Nw6eyCD+9dv9jp49ARSMrKIiolr8fFWi0F6vJtol1pnIiJyaikYSYd0dJZoV2ElD6/M5VC5DwO4eEwcWd6Pyd+4h4HnX4rFYsEwjFZDkcdZ3zqzW9U6ExGRU0/BSNqlo7NEobDJK5vyeWHdQUJhk4QIB99fMIwh0QZvLXsHgMryUmLiE1s9R3K0k+Qop1pnIiJy2igYyXF1dJaoyOtn6Zu5bC/wAnDO4ARumTOEqIZW2NS55xMZE0dEVEyLj7dZDdLj3I3jRUREThcFI2lVKGxSUO6jvKZ9s0QAq3OKeOqdPVTXhnDbrdw4KRZr/iZMXzK4EgBISc9q9fERTisZap2JiEgX0aePtMjrryO3sLLdoajKH+TB5Tt5eGUu1bUhhqdE8dv/mUBU+S4qSo/y8bp323y8YUBKtJNBSZEKRSIi0mU0YyRNnMgs0Za8ch59M5eS6losBvzPGZl8dUoGVotB3PR5ONa7GHPmjFYfb7MaZMR7iHTqx1FERLqWPomkkddfx6EyH8FQ+64lCgRD/OWDA/y7YZ+z1BgXN02MJNoowWrJBMDljmByK5u/AkS6bGTEubFplkhERLoBBSM5oVmiPUereHhlLnmln+1zdsmISN577UUMwyA+qR/xyf1bfbxhHLvrzHXS9YuIiHQWBaM+rqOzRKGwySub8/nrRwcJhk1iPXa+O3coU7LqF2vMGDwCm91OTHxSq+ew2wwy4jxEqHUmIiLdjD6Z+qhgKMzhCn+HZomOeP08sjKXHYfrb8M/a1A8Xx1iZVB6dOOYKTMXYlhab4tFuWykq3UmIiLdlIJRH1Thq6OgvP2zRKZp8tbOIp55dy++uvrb8L85YxBJFZ/y8Zot1JRMYPzZswFaDUX1d525SIpydtbLEBER6XQKRn3IicwSVfjqyH57Nx/sLQFgVP9ovr9gGP2iXRzJq2Hvp1txuNyYptnqCtUOm4WMeDceh37cRESke9MnVR/R0VkigA37S/ntql2U19Rhsxh87cwMzhseS2TDBdP9Mgay8LJrW13BGiDGbSctzo3Vom09RESk+1Mw6uWCoTAF5X4qfO2fJfLXhfjTe/t445MjAGTEe7h1ZgbFH69h7d5y5i3+OnZHfUustVBkGNA/xkVCpFpnIiLScygY9WIVNfV7nIXC7Z8lyi2sZOnKXA6V+wD40vhUrj57AEaojv3ecgL+GsqLi0hKzWj1HA6bhcx4D26H9aRfg4iIyOmkYNQLncgsUShs8rcNeby4/iBhExIiHHx33hAmZtbfho/NytR5F2Cz2YmKjW/1PLEeO6mxap2JiEjPpGDUy5zILFFBuY+lK3PJKawEYMbQRK6aEMeO99/giDGNfhkDAYhLTGn1HIYBqbFu4iMcJ/cCREREupCCUS9xIrNEpmny3+1H+OPafQSCYSIcVm6eNZjZw5PZ9uE7VJQe5ZN1a0lJz2r1jjMAp72+deayq3UmIiI9m4JRL1BeU0tBub9Ds0Rl1bX8btUuNhwoA2BcWgzfmz+scZ2h0VPOIRwOMXzC1DZDUVyEndQYNxa1zkREpBdQMOrB6kJhCsp9eH3BDj3ug70lPL5qF15/ELvV4OqzszinHxR+uo6kM2cAYLXZmDBtbqvnMAxIj3MT61HrTEREeg8Fox7qRGaJamqD/GHNPlZ+WghAVoKH2xYOJ9kNy//2J8KhELGJKaQPGtbmedwOCxnxHpw2tc5ERKR3UTDqYU50lmjHYS9LV+ZQ6A1gAF+ZlMbXpw7A3rBn2fDxZ1JVUUZK+oA2zxMf6SA1xtVme01ERKSnUjDqQcqqaymo8BEOt/8xdaEw/7fuIP/YlE/YhOQoJ9+fP4z4YDGhWj92tweAERPObDPsWCyQHuchxm0/2ZchIiLSbSkY9QB1oTCHynxU+js2S5RXWsPDK3PYc7QagLkjkvnmjEHk79zMhxveIyU9i2kLv4xhGG2GIrfDSma8B4et5Q1iRUREegsFo27uRGaJwqbJf7Yd5rn391MbChPltHHLnCGcMyQRqN/jbOeWj4iJS2hz81eAxCgH/aLVOhMRkb5BwaibOtFZopKqAI++tYsteeUATMqM49a5Q3CGahrHxMQnsvCy63B7Ilo9j9VikB7vJtql1pmIiPQdCkbd0InMEgGs2XWUJ1bvoSoQxGGzcP20LBaMSGDjO8s5ejifeYu/TkR0/aavbYWiCKeVjHhP44XZIiIifYWCUTdSG6y/46yjs0RVgSBPv7uH1TlHARiSHMmSBcPIiPMQDocJ+H2EQyHKSgobg1FrkqOdJEc51ToTEZE+ScGoG9ldVNWhdYkAPs4vZ+mbuyiuCmAx4LIpGXx1Uhr2hjWGLBYLZ84+j9paP7EJya2ex2Y1yIj3EOnUj4SIiPRd+hTsRsJm+0NRXSjMXz44wL+2HMIE+se4WDJ/GBmRJu//9x9kDBrO4NETAPBEReMhutVzRbpsZMS5sal1JiIifZyCUQ+0r7iapStz2F9Sf0H1otH9uOGcgbgdVvbs2Epp0WGqvRUMGDYam731i6cN41jrzHW6ShcREenWFIx6kLBpsmzzIZ7/8ADBsEms28535g7hzIEJjWMGjRyHv6aarOFthyK7zSAjzkOEWmciIiKN9KnYQxR5/Tz61i4+PlQBwNSB8Xx7zhCoKWfDu8uZNH0BFosFwzAYPWVam+eKdttIj/NgtegCaxERkc9TMOrmTNPk7ZyjPP3uHmpqQ7jsFm6cPoiFo1IIhYIs/+c/Cfh9RMXEM3z8GW2eyzCgX4yLxEjnaapeRESkZ1Ew6sa8vjqeeGcP7+0uBmBEvyiWLBhG/xg3ADabnfFnzyZ/by4DR4xt81wOm4XMeA9uh/WU1y0iItJTKRh1U5sOlvHbN3dRWlOL1WJwxZmZXDopneKCg1SEIoiJr9/eI33QcNIGDmtz3aEYt520OLdaZyIiIsehYNTN+OtCPPf+fv7z8WEA0mLd/GDBMIamRHEgdzsb16wkOjaBOV++Aqut/q+vtVBkGJAa6yY+wnHa6hcREenJFIy6kd1FVTy0Iof8Mh8AF47tzzXTsnDZ69tfKRkDcbo9JPRLO+65nPb61tmxx4qIiMjxKRh1A8FQmKfe2cMjb+4iFDaJ9zj47ryhTBoQR0VpMa6GtpnL7WH+V67C6XK3eb5Yj520WDcWtc5EREQ6pM8tdZyXl8fs2bMZNWoU48aN4+9//3tXl8TOI5UsXZlLKGxyzuAEHrtiIhMyolm/+r+8tewFio8cahzbVigyDMiId5MR71EoEhEROQF9bsbIZrPx6KOPMmHCBIqKipg0aRLnn38+ERGt7zZ/qo1Ji+G2RcMJhkxmD0tqvGbIMAwMoKK0mMTjtM9cdgsZap2JiIiclD4XjPr370///v0BSE5OJj4+ntLS0i4NRgD/b/YQPs4vJxwKY1jrw834s+cwaOQ44pP7t/nY+EgHqTGuNu9MExERkePrdq20d999l4suuojU1FQMw2DZsmXNxjzxxBMMHDgQl8vF5MmTWbNmzQk914YNGwiHw2RkZJxk1SevsrKSNW+8wraP3m08Znc42gxFFgtkxntIi3UrFImIiHSCbjdjVF1dzfjx47nuuuu45JJLmn3/pZde4nvf+x5PPPEE55xzDk8//TTnnXceO3bsIDMzE4DJkycTCASaPXbFihWkpqYCUFJSwtVXX80f/vCHVmsJBAJNzuP1ek/25bWqsLCQowV5lBYdZvj4M3BHRLY53u2wkhHvxmlT60xERKSzGKZpml1dRGsMw+Cf//wnixcvbjw2depUJk2axJNPPtl4bOTIkSxevJj77ruvXecNBAIsWLCAb3zjG1x11VWtjrvrrru4++67mx2vqKggOjq6/S+knZateIfk1EyiYuPbHJcY5aBftFpnIiIi7eH1eomJiWnX53e3a6W1pba2lo0bN7Jw4cImxxcuXMj777/frnOYpsm1117L3Llz2wxFAD/96U+pqKho/JWXl3fCtbfHkNET2gxFVovBgEQP/WPUOhMRETkVul0rrS3FxcWEQiFSUlKaHE9JSeHIkSPtOsd7773HSy+9xLhx4xqvX3r++ecZO7b5XmNOpxOns3tsuOpxWsmM92C39qgsKyIi0qP0qGB0zBdnS0zTbPcMyvTp0wmHw6eirFMmOdpJcpRTs0QiIiKnWI8KRomJiVit1mazQ0VFRc1mkXoDm9UgI95DpLNH/TWJiIj0WD2qL+NwOJg8eTIrV65scnzlypVMmzati6o6NSJdNoYkRyoUiYiInEbd7lO3qqqK3bt3N369b98+tmzZQnx8PJmZmSxZsoSrrrqKKVOmcPbZZ/PMM89w8OBBbr755i6suvMYxrHWmaurSxEREelzul0w2rBhA3PmzGn8esmSJQBcc801PPvss1x++eWUlJTwy1/+ksOHDzNmzBhef/11BgwY0FUldxq71UJ6nJsIzRKJiIh0iW69jlF305F1EE5EKGxi1eavIiIinarXrmPUVbKzsxk1ahRnnHHGKX0ehSIREZGupRmjDjjVM0YiIiLS+TRjJCIiInICFIxEREREGigYiYiIiDRQMBIRERFpoGAkIiIi0kDBSERERKSBgpGIiIhIAwUjERERkQYKRu1wula+FhERka6lla87QCtfi4iI9Dxa+VpERETkBCgYiYiIiDRQMBIRERFpYOvqAnqSY5djeb3eLq5ERERE2uvY53Z7LqtWMOqAyspKADIyMrq4EhEREemoyspKYmJi2hyju9I6IBwOU1BQQFRUFIZhHHf8GWecwfr169t1bq/XS0ZGBnl5ebrj7QR15M+7u+kOtZ+OGk7Fc3TWOU/2PCfyeL1HnF7d4d/ZieoOtZ+uGk7F80yZMoVVq1aRmpqKxdL2VUSaMeoAi8VCenp6u8dbrdYOv4FFR0frTe8Encifd3fRHWo/HTWciuforHOe7HlO5PF6jzi9usO/sxPVHWo/XTWciuex2Wzt/vzWxden0C233NLVJfQpPfnPuzvUfjpqOBXP0VnnPNnznMjju8Pfe1/Sk/+8u0Ptp6uGrn6fUCutm9DikSLSFr1HiJwemjHqJpxOJ7/4xS9wOp1dXYqIdEN6jxA5PTRjJCIiItJAM0YiIiIiDRSMRERERBooGImIiIg0UDASERERaaBgJCIiItJAwaiHycvLY/bs2YwaNYpx48bx97//vatLEpFu6OKLLyYuLo5LL720q0sR6VF0u34Pc/jwYQoLC5kwYQJFRUVMmjSJnJwcIiIiuro0EelG3n77baqqqnjuued4+eWXu7ockR5DM0Y9TP/+/ZkwYQIAycnJxMfHU1pa2rVFiUi3M2fOHKKiorq6DJEeR8Gok7377rtcdNFFpKamYhgGy5YtazbmiSeeYODAgbhcLiZPnsyaNWtO6Lk2bNhAOBwmIyPjJKsWkdPpdL5PiEjHKBh1surqasaPH8/jjz/e4vdfeuklvve97/Hzn/+czZs3M2PGDM477zwOHjzYOGby5MmMGTOm2a+CgoLGMSUlJVx99dU888wzp/w1iUjnOl3vEyLScbrG6BQyDIN//vOfLF68uPHY1KlTmTRpEk8++WTjsZEjR7J48WLuu+++dp03EAiwYMECvvGNb3DVVVd1dtkichqdqvcJgNWrV/P444/rGiORDtCM0WlUW1vLxo0bWbhwYZPjCxcu5P3332/XOUzT5Nprr2Xu3LkKRSK9UGe8T4jIiVMwOo2Ki4sJhUKkpKQ0OZ6SksKRI0fadY733nuPl156iWXLljFhwgQmTJjAxx9/fCrKFZEu0BnvEwCLFi3isssu4/XXXyc9PZ3169d3dqkivZKtqwvoiwzDaPK1aZrNjrVm+vTphMPhU1GWiHQjJ/M+AbB8+fLOLkmkT9CM0WmUmJiI1Wpt9r++oqKiZv87FJG+Se8TIl1Lweg0cjgcTJ48mZUrVzY5vnLlSqZNm9ZFVYlId6L3CZGupVZaJ6uqqmL37t2NX+/bt48tW7YQHx9PZmYmS5Ys4aqrrmLKlCmcffbZPPPMMxw8eJCbb765C6sWkdNJ7xMi3Zdu1+9kq1evZs6cOc2OX3PNNTz77LNA/cJtDzzwAIcPH2bMmDE88sgjzJw58zRXKiJdRe8TIt2XgpGIiIhIA11jJCIiItJAwUhERESkgYKRiIiISAMFIxEREZEGCkYiIiIiDRSMRERERBooGImIiIg0UDASERERaaBgJCIiItJAwUhERESkgYKRiIiISAMFIxHpcQzDaPPXtdde29UlikgPZevqAkREOurw4cONv3/ppZe48847ycnJaTzmdrubPaa2thaHw3Fa6hORnkszRiLS4/Tr16/xV0xMDIZhNDs2e/Zsvv3tb7NkyRISExNZsGABAFlZWTz66KNNzjdhwgTuuusuAEzT5IEHHmDQoEG43W7Gjx/Pyy+/3GY9a9euxW63EwgEGo/t27cPwzA4cOBAp752ETm1NGMkIr3Wc889x7e+9S3ee+89TNNs12Nuv/12XnnlFZ588kmGDh3Ku+++y5VXXklSUhKzZs1q8TFbtmxh5MiROJ3OJsdiY2MZMGBAp7wWETk9FIxEpNcaMmQIDzzwQLvHV1dXs3TpUlatWsXZZ58NwKBBg1i7di1PP/10q8Fo69atTJw4scmxLVu2MH78+BMvXkS6hIKRiPRaU6ZM6dD4HTt24Pf7G9tux9TW1jYLPp+3ZcsWvva1rzU5tnnzZgUjkR5IwUhEeq2IiIhmxywWS7O2Wl1dHQDhcBiA1157jbS0tCZjPt8m+7xQKMT27dubBadNmzZx8cUXn3DtItI1FIxEpE9JSkpqcleb1+tl3759AIwaNQqn08nBgwdbbZt9UU5ODj6fj9TU1MZjH3zwAYcOHdKMkUgPpGAkIn3K3LlzefbZZ7nooouIi4vjjjvuwGq1AhAVFcVtt93G97//fcLhMNOnT8fr9fL+++8TGRnJNddc0+x8W7ZsAeCxxx7j1ltvZffu3dx6660ATe5SE5GeQcFIRPqUn/70p+zdu5cLL7yQmJgY7rnnnsYZI4B77rmH5ORk7rvvPvbu3UtsbCyTJk3iZz/7WYvn27JlCwsWLGDfvn2MGTOGUaNG8Zvf/Ibrr7+e7Ozsxou4RaRnMMz23sMqIiLNLFq0iEmTJnHfffd1dSki0gm0wKOIyEnYunUr48aN6+oyRKSTKBiJiJygI0eOUFhYqGAk0ouolSYiIiLSQDNGIiIiIg0UjEREREQaKBiJiIiINFAwEhEREWmgYCQiIiLSQMFIREREpIGCkYiIiEgDBSMRERGRBgpGIiIiIg0UjEREREQa/H9OllBiFFotZwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_mu_plot(mu_hats, title='2D Correlated Gaussian Case')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fcedcdf-fd85-420e-9042-d28889c96624",
   "metadata": {},
   "source": [
    "### Analytic Distributions -  2D Gaussian Signal + Exponential Background Case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e99cba98-7f89-4729-a11b-7fc443da04d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "class DistributionModel:\n",
    "    def __init__(self, seed=None):\n",
    "        self.seed = seed\n",
    "        self.random_state = np.random.RandomState(seed) if seed is not None else None\n",
    "\n",
    "    def rvs(self, size):\n",
    "        raise NotImplementedError\n",
    "\n",
    "class ExponentialModel(DistributionModel):\n",
    "    def __init__(self, scale, seed=None):\n",
    "        super().__init__(seed)\n",
    "        self.scale = scale\n",
    "\n",
    "    def rvs(self, size, random_state=None):\n",
    "        random_state = random_state or self.random_state\n",
    "        return expon(scale=self.scale).rvs(size=(size, 2), random_state=random_state)\n",
    "\n",
    "    def pdf(self, x):\n",
    "        # The PDF of the exponential distribution for each independent variable:\n",
    "        # f(x) = (1 / scale) * exp(-x / scale) for x > 0\n",
    "        # In 2D, assuming independence, the joint PDF is the product of the marginal PDFs.\n",
    "        pdf_x1 = (1 / self.scale) * np.exp(-x[:, 0] / self.scale)\n",
    "        pdf_x2 = (1 / self.scale) * np.exp(-x[:, 1] / self.scale)\n",
    "        return pdf_x1 * pdf_x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fb71083d-2401-4848-b411-a4cf5231974c",
   "metadata": {},
   "outputs": [],
   "source": [
    "mu_inj_list = np.logspace(-2, -0.3, 10)\n",
    "N_trial = 10\n",
    "N_B = 100000\n",
    "seed = 2024\n",
    "\n",
    "mu_S = [3, 3]\n",
    "cov_S = np.array([[1, 0], [0, 1]])\n",
    "model_S = multivariate_normal(mean=mu_S, cov=cov_S, seed=seed)\n",
    "\n",
    "scale_B = (10 - 1) / np.log(10)\n",
    "model_B = ExponentialModel(scale=scale_B, seed=seed)\n",
    "\n",
    "R = get_R(model_B, N_B)\n",
    "D = get_D(model_S, model_B, N_B, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c4282d01-ff1d-417c-87b3-aaea05dd2f21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'count')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(R[:, 0], alpha=0.5, range=(0, 20), bins=40, label='Reference')\n",
    "plt.hist(D[:, 0], alpha=0.5, range=(0, 20), bins=40, label='Data')\n",
    "plt.legend()\n",
    "plt.xlabel('x')\n",
    "plt.xlabel('count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "39bdad6e-bc25-4eef-91b7-13b980e9d5f8",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running trial 1 with mu = 0.01\n",
      "Running trial 8 with mu = 0.01\n",
      "Running trial 2 with mu = 0.01\n",
      "Running trial 3 with mu = 0.01\n",
      "Running trial 4 with mu = 0.01\n",
      "Running trial 5 with mu = 0.01\n",
      "Running trial 6 with mu = 0.01\n",
      "Running trial 7 with mu = 0.01\n",
      "Running trial 9 with mu = 0.01\n",
      "Running trial 10 with mu = 0.01\n",
      "Running trial 1 with mu = 0.015448591479026755\n",
      "Running trial 2 with mu = 0.015448591479026755\n",
      "Running trial 4 with mu = 0.015448591479026755\n",
      "Running trial 3 with mu = 0.015448591479026755\n",
      "Running trial 5 with mu = 0.015448591479026755\n",
      "Running trial 6 with mu = 0.015448591479026755\n",
      "Running trial 7 with mu = 0.015448591479026755\n",
      "Running trial 8 with mu = 0.015448591479026755\n",
      "Running trial 9 with mu = 0.015448591479026755\n",
      "Running trial 10 with mu = 0.015448591479026755\n",
      "Running trial 1 with mu = 0.023865897868585808\n",
      "Running trial 2 with mu = 0.023865897868585808\n",
      "Running trial 3 with mu = 0.023865897868585808\n",
      "Running trial 4 with mu = 0.023865897868585808\n",
      "Running trial 5 with mu = 0.023865897868585808\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n",
      "/tmp/ipykernel_174446/909118199.py:50: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
      "  res = minimize_scalar(func, bounds=(1e-6, 1 - 1e-6), tol=1e-6)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running trial 6 with mu = 0.023865897868585808\n",
      "Running trial 7 with mu = 0.023865897868585808\n",
      "Running trial 8 with mu = 0.023865897868585808\n",
      "Running trial 9 with mu = 0.023865897868585808\n",
      "Running trial 10 with mu = 0.023865897868585808\n",
      "Running trial 1 with mu = 0.036869450645195756\n",
      "Running trial 2 with mu = 0.036869450645195756\n",
      "Running trial 3 with mu = 0.036869450645195756\n",
      "Running trial 4 with mu = 0.036869450645195756\n",
      "Running trial 5 with mu = 0.036869450645195756\n",
      "Running trial 7 with mu = 0.036869450645195756\n",
      "Running trial 6 with mu = 0.036869450645195756\n",
      "Running trial 8 with mu = 0.036869450645195756\n",
      "Running trial 9 with mu = 0.036869450645195756\n",
      "Running trial 10 with mu = 0.036869450645195756\n",
      "Running trial 1 with mu = 0.056958108107376865\n",
      "Running trial 2 with mu = 0.056958108107376865\n",
      "Running trial 3 with mu = 0.056958108107376865\n",
      "Running trial 4 with mu = 0.056958108107376865\n",
      "Running trial 5 with mu = 0.056958108107376865\n",
      "Running trial 6 with mu = 0.056958108107376865\n",
      "Running trial 7 with mu = 0.056958108107376865\n",
      "Running trial 8 with mu = 0.056958108107376865\n",
      "Running trial 9 with mu = 0.056958108107376865\n",
      "Running trial 10 with mu = 0.056958108107376865\n",
      "Running trial 1 with mu = 0.0879922543569107\n",
      "Running trial 2 with mu = 0.0879922543569107\n",
      "Running trial 3 with mu = 0.0879922543569107\n",
      "Running trial 4 with mu = 0.0879922543569107\n",
      "Running trial 5 with mu = 0.0879922543569107\n",
      "Running trial 6 with mu = 0.0879922543569107\n",
      "Running trial 7 with mu = 0.0879922543569107\n",
      "Running trial 9 with mu = 0.0879922543569107\n",
      "Running trial 10 with mu = 0.0879922543569107\n",
      "Running trial 8 with mu = 0.0879922543569107\n",
      "Running trial 1 with mu = 0.13593563908785256\n",
      "Running trial 2 with mu = 0.13593563908785256\n",
      "Running trial 3 with mu = 0.13593563908785256\n",
      "Running trial 5 with mu = 0.13593563908785256\n",
      "Running trial 4 with mu = 0.13593563908785256\n",
      "Running trial 6 with mu = 0.13593563908785256\n",
      "Running trial 7 with mu = 0.13593563908785256\n",
      "Running trial 8 with mu = 0.13593563908785256\n",
      "Running trial 9 with mu = 0.13593563908785256\n",
      "Running trial 10 with mu = 0.13593563908785256\n",
      "Running trial 1 with mu = 0.21000141557086555\n",
      "Running trial 2 with mu = 0.21000141557086555\n",
      "Running trial 3 with mu = 0.21000141557086555\n",
      "Running trial 4 with mu = 0.21000141557086555\n",
      "Running trial 5 with mu = 0.21000141557086555\n",
      "Running trial 6 with mu = 0.21000141557086555\n",
      "Running trial 7 with mu = 0.21000141557086555\n",
      "Running trial 8 with mu = 0.21000141557086555\n",
      "Running trial 9 with mu = 0.21000141557086555\n",
      "Running trial 10 with mu = 0.21000141557086555\n",
      "Running trial 1 with mu = 0.324422607917163\n",
      "Running trial 2 with mu = 0.324422607917163\n",
      "Running trial 3 with mu = 0.324422607917163\n",
      "Running trial 4 with mu = 0.324422607917163\n",
      "Running trial 5 with mu = 0.324422607917163\n",
      "Running trial 6 with mu = 0.324422607917163\n",
      "Running trial 7 with mu = 0.324422607917163\n",
      "Running trial 8 with mu = 0.324422607917163\n",
      "Running trial 9 with mu = 0.324422607917163\n",
      "Running trial 10 with mu = 0.324422607917163\n",
      "Running trial 1 with mu = 0.5011872336272722\n",
      "Running trial 2 with mu = 0.5011872336272722\n",
      "Running trial 3 with mu = 0.5011872336272722\n",
      "Running trial 4 with mu = 0.5011872336272722\n",
      "Running trial 5 with mu = 0.5011872336272722\n",
      "Running trial 6 with mu = 0.5011872336272722\n",
      "Running trial 7 with mu = 0.5011872336272722\n",
      "Running trial 8 with mu = 0.5011872336272722\n",
      "Running trial 9 with mu = 0.5011872336272722\n",
      "Running trial 10 with mu = 0.5011872336272722\n"
     ]
    }
   ],
   "source": [
    "mu_hats = scan_mu_hat(mu_inj_list, N_B, N_trial, model_S, model_B, max_workers=25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "8a1eb98e-1f94-4772-8b46-b01fe28ffc6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_mu_plot(mu_hats, title='2D Gaussian Signal + Exponential Background Case')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5aedaab7-f207-4081-9610-f60033069d62",
   "metadata": {},
   "source": [
    "### Model Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1648e29e-1ae8-4a86-afa4-fdb6a9fd0e24",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2024-10-06 01:44:06.060433: E external/local_xla/xla/stream_executor/cuda/cuda_dnn.cc:9261] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered\n",
      "2024-10-06 01:44:06.061489: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:607] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered\n",
      "2024-10-06 01:44:06.155935: E external/local_xla/xla/stream_executor/cuda/cuda_blas.cc:1515] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered\n",
      "2024-10-06 01:44:06.401773: I tensorflow/core/platform/cpu_feature_guard.cc:182] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations.\n",
      "To enable the following instructions: AVX2 FMA, in other operations, rebuild TensorFlow with the appropriate compiler flags.\n",
      "2024-10-06 01:44:08.707442: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Could not find TensorRT\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "from sklearn.model_selection import train_test_split\n",
    "from scipy.stats import multivariate_normal, expon\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "seed = 2024\n",
    "\n",
    "# Signal (S): 2D Gaussian with slight correlation\n",
    "mu_S = [3, 3]\n",
    "cov_S = np.array([[1.0, 0.5], [0.5, 1.0]])  # Slight correlation\n",
    "N_S = 100_000  # 100k signals\n",
    "\n",
    "# Background (B): 2D Exponential, no correlation\n",
    "scale_B = (10 - 1) / np.log(10)\n",
    "N_B = 1_000_000  # 1M backgrounds\n",
    "\n",
    "# Generate the signal and background samples\n",
    "signal_data = multivariate_normal(mean=mu_S, cov=cov_S).rvs(size=N_S)\n",
    "background_data = expon(scale=scale_B).rvs(size=(N_B, 2))\n",
    "\n",
    "signal_labels = np.ones(N_S)  \n",
    "background_labels = np.zeros(N_B) \n",
    "\n",
    "X = np.concatenate([signal_data, background_data], axis=0)\n",
    "y = np.concatenate([signal_labels, background_labels], axis=0)\n",
    "\n",
    "# 2. Split into train, validation, and test datasets (50%, 25%, 25%)\n",
    "X_train, X_temp, y_train, y_temp = train_test_split(X, y, test_size=0.5, random_state=seed)\n",
    "X_val, X_test, y_val, y_test = train_test_split(X_temp, y_temp, test_size=0.5, random_state=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a7766043-5b77-44bd-99e8-f3e91b310caa",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2024-10-06 01:44:14.662553: W tensorflow/core/common_runtime/gpu/gpu_device.cc:2256] Cannot dlopen some GPU libraries. Please make sure the missing libraries mentioned above are installed properly if you would like to use GPU. Follow the guide at https://www.tensorflow.org/install/gpu for how to download and setup the required libraries for your platform.\n",
      "Skipping registering GPU devices...\n"
     ]
    }
   ],
   "source": [
    "model = tf.keras.Sequential([\n",
    "    tf.keras.layers.Dense(64, activation='relu', input_shape=(2,)),\n",
    "    tf.keras.layers.Dense(32, activation='relu'),\n",
    "    tf.keras.layers.Dense(1, activation='sigmoid') \n",
    "])\n",
    "\n",
    "model.compile(optimizer='adam', loss='binary_crossentropy', metrics=['accuracy'])\n",
    "\n",
    "early_stopping = tf.keras.callbacks.EarlyStopping(\n",
    "    monitor='val_loss',  \n",
    "    patience=10,        \n",
    "    restore_best_weights=True\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3f7d7c61-4655-4daa-9645-e3a2ae4a9b59",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/100\n",
      "4297/4297 [==============================] - 5s 998us/step - loss: 0.1948 - accuracy: 0.9097 - val_loss: 0.1813 - val_accuracy: 0.9131\n",
      "Epoch 2/100\n",
      "4297/4297 [==============================] - 4s 954us/step - loss: 0.1826 - accuracy: 0.9123 - val_loss: 0.1815 - val_accuracy: 0.9134\n",
      "Epoch 3/100\n",
      "4297/4297 [==============================] - 4s 920us/step - loss: 0.1822 - accuracy: 0.9127 - val_loss: 0.1815 - val_accuracy: 0.9131\n",
      "Epoch 4/100\n",
      "4297/4297 [==============================] - 4s 888us/step - loss: 0.1820 - accuracy: 0.9129 - val_loss: 0.1807 - val_accuracy: 0.9134\n",
      "Epoch 5/100\n",
      "4297/4297 [==============================] - 4s 928us/step - loss: 0.1818 - accuracy: 0.9129 - val_loss: 0.1812 - val_accuracy: 0.9135\n",
      "Epoch 6/100\n",
      "4297/4297 [==============================] - 4s 914us/step - loss: 0.1818 - accuracy: 0.9128 - val_loss: 0.1807 - val_accuracy: 0.9130\n",
      "Epoch 7/100\n",
      "4297/4297 [==============================] - 4s 923us/step - loss: 0.1817 - accuracy: 0.9129 - val_loss: 0.1809 - val_accuracy: 0.9135\n",
      "Epoch 8/100\n",
      "4297/4297 [==============================] - 4s 914us/step - loss: 0.1818 - accuracy: 0.9128 - val_loss: 0.1806 - val_accuracy: 0.9134\n",
      "Epoch 9/100\n",
      "4297/4297 [==============================] - 4s 934us/step - loss: 0.1817 - accuracy: 0.9127 - val_loss: 0.1807 - val_accuracy: 0.9135\n",
      "Epoch 10/100\n",
      "4297/4297 [==============================] - 4s 934us/step - loss: 0.1817 - accuracy: 0.9126 - val_loss: 0.1815 - val_accuracy: 0.9131\n",
      "Epoch 11/100\n",
      "4297/4297 [==============================] - 4s 902us/step - loss: 0.1816 - accuracy: 0.9129 - val_loss: 0.1807 - val_accuracy: 0.9133\n",
      "Epoch 12/100\n",
      "4297/4297 [==============================] - 4s 936us/step - loss: 0.1817 - accuracy: 0.9127 - val_loss: 0.1807 - val_accuracy: 0.9136\n",
      "Epoch 13/100\n",
      "4297/4297 [==============================] - 4s 927us/step - loss: 0.1816 - accuracy: 0.9127 - val_loss: 0.1804 - val_accuracy: 0.9134\n",
      "Epoch 14/100\n",
      "4297/4297 [==============================] - 4s 960us/step - loss: 0.1816 - accuracy: 0.9129 - val_loss: 0.1809 - val_accuracy: 0.9129\n",
      "Epoch 15/100\n",
      "4297/4297 [==============================] - 4s 974us/step - loss: 0.1816 - accuracy: 0.9128 - val_loss: 0.1804 - val_accuracy: 0.9133\n",
      "Epoch 16/100\n",
      "4297/4297 [==============================] - 4s 967us/step - loss: 0.1816 - accuracy: 0.9128 - val_loss: 0.1810 - val_accuracy: 0.9132\n",
      "Epoch 17/100\n",
      "4297/4297 [==============================] - 4s 960us/step - loss: 0.1816 - accuracy: 0.9127 - val_loss: 0.1805 - val_accuracy: 0.9134\n",
      "Epoch 18/100\n",
      "4297/4297 [==============================] - 4s 962us/step - loss: 0.1815 - accuracy: 0.9127 - val_loss: 0.1814 - val_accuracy: 0.9132\n",
      "Epoch 19/100\n",
      "4297/4297 [==============================] - 4s 989us/step - loss: 0.1815 - accuracy: 0.9129 - val_loss: 0.1810 - val_accuracy: 0.9132\n",
      "Epoch 20/100\n",
      "4297/4297 [==============================] - 4s 946us/step - loss: 0.1815 - accuracy: 0.9128 - val_loss: 0.1816 - val_accuracy: 0.9133\n",
      "Epoch 21/100\n",
      "4297/4297 [==============================] - 4s 940us/step - loss: 0.1815 - accuracy: 0.9129 - val_loss: 0.1808 - val_accuracy: 0.9134\n",
      "Epoch 22/100\n",
      "4297/4297 [==============================] - 4s 967us/step - loss: 0.1815 - accuracy: 0.9128 - val_loss: 0.1808 - val_accuracy: 0.9133\n",
      "Epoch 23/100\n",
      "4297/4297 [==============================] - 4s 971us/step - loss: 0.1815 - accuracy: 0.9130 - val_loss: 0.1805 - val_accuracy: 0.9134\n"
     ]
    }
   ],
   "source": [
    "history = model.fit(\n",
    "    X_train, y_train,\n",
    "    validation_data=(X_val, y_val),\n",
    "    epochs=100,  # Set a large number of epochs, early stopping will handle when to stop\n",
    "    batch_size=128,\n",
    "    callbacks=[early_stopping]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cf6c2751-45de-4460-82ae-2794ae04b055",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8594/8594 [==============================] - 5s 538us/step - loss: 0.1811 - accuracy: 0.9131\n",
      "Test Accuracy: 91.31%\n"
     ]
    }
   ],
   "source": [
    "test_loss, test_acc = model.evaluate(X_test, y_test)\n",
    "print(f\"Test Accuracy: {test_acc * 100:.2f}%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "75e53bc6-8899-4f45-a0a0-51c3ca2dbfd4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(history.history['loss'], label='Train Loss')\n",
    "plt.plot(history.history['val_loss'], label='Validation Loss')\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Loss')\n",
    "plt.legend()\n",
    "plt.title('Training and Validation Loss')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "552d7956-5a74-4f32-872e-ed9dc7a54b7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Craete weakly datasets\n",
    "\n",
    "S_test = X_test[y_test == 1]\n",
    "B_test = X_test[y_test == 0] \n",
    "\n",
    "mu = 0.1\n",
    "N_B = 100_000\n",
    "N_S = int(mu / (1 - mu) * N_B)\n",
    "\n",
    "D = np.concatenate([S_test[:N_S], B_test[:N_B]], axis=0)\n",
    "R = B_test[N_B : 2 * N_B]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fe487ca4-5cd7-4725-b7c1-26ad794f0656",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'x')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(R[:, 0], alpha=0.5, range=(0, 20), bins=40, label='Reference')\n",
    "plt.hist(D[:, 0], alpha=0.5, range=(0, 20), bins=40, label='Data')\n",
    "plt.legend()\n",
    "plt.xlabel('x')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13e04204-40f4-47a7-b847-5b6522119119",
   "metadata": {},
   "source": [
    "Likelihood ratio from supervised model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "102e5801-ccfb-4138-ad03-e970a61e3fe2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3125/3125 [==============================] - 2s 493us/step\n"
     ]
    }
   ],
   "source": [
    "# supervised output\n",
    "FS_ref = model.predict(R).flatten()\n",
    "kappa = 1 / np.mean(FS_ref / (1 - FS_ref))\n",
    "likelihood = kappa * (FS_ref / (1 - FS_ref))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf714ad4-7be7-4337-9207-92940bf1c709",
   "metadata": {},
   "source": [
    "Likelihood ratio ($p_S / p_B$) from analytic formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "9a59ca75-8ee9-4df4-8c43-e0dd673e66fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate the analytic pS/pB\n",
    "\n",
    "mu_S = [3, 3]\n",
    "cov_S = np.array([[1.0, 0.5], [0.5, 1.0]])  \n",
    "model_S = multivariate_normal(mean=mu_S, cov=cov_S)\n",
    "\n",
    "scale_B = (10 - 1) / np.log(10) \n",
    "model_B = expon(scale=scale_B)\n",
    "\n",
    "pS = model_S.pdf(R)\n",
    "pB_x1 = model_B.pdf(R[:, 0])\n",
    "pB_x2 = model_B.pdf(R[:, 1])\n",
    "pB = pB_x1 * pB_x2\n",
    "\n",
    "# analytic\n",
    "pS_over_pB = pS / pB"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a8f9104-0097-4faf-9fb7-a5954c57d853",
   "metadata": {},
   "source": [
    "Checking normalization of pS/pB from ML model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "256c96e5-8851-4345-abf3-d7ff29dc2819",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N_ref: 100000, integral of pS/pB : 100597.87399038428\n"
     ]
    }
   ],
   "source": [
    "print(f'N_ref: {R.shape[0]}, integral of pS/pB : {pS_over_pB.sum()}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c507e6b1-79d6-435f-b37f-b17957294d79",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N_ref: 100000, integral of likelihood from ML model : 99999.9921875\n"
     ]
    }
   ],
   "source": [
    "print(f'N_ref: {R.shape[0]}, integral of likelihood from ML model : {likelihood.sum()}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b16af892-61b6-452b-8a48-ce5c6be91709",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_210780/3257572001.py:2: RuntimeWarning: divide by zero encountered in divide\n",
      "  ratio = pS_over_pB / likelihood\n",
      "/tmp/ipykernel_210780/3257572001.py:2: RuntimeWarning: invalid value encountered in divide\n",
      "  ratio = pS_over_pB / likelihood\n"
     ]
    }
   ],
   "source": [
    "# Now compare term by term\n",
    "ratio = pS_over_pB / likelihood\n",
    "ratio = ratio[np.isfinite(ratio)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "0660582c-4cf8-42a0-911a-9a677c4175c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'count')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0b98+9enTRwUFBYqLi5MkFRQUKCEhQV9++aWio6P14YcfKjk5WaWlpYqMjJQkZWVlafLkyaqoqFBwcPAV+19dXS2HwyGXy2WpvjlunruxVdu70OGFY9qsbQAAPJ3V92+PuqfJ5XJJkjp37ixJOnTokMrLy5WYmGjW2O12DRkyRFu3bpUkFRYWqr6+3q0mMjJSMTExZs22bdvkcDjMwCRJ8fHxcjgcbjUxMTFmYJKkpKQk1dbWqrCwsMn+1tbWqrq62u0BAACuTx4TmgzD0KxZs3TPPfcoJiZGklReXi5JCg8Pd6sNDw83t5WXl8vf318hISGXrQkLC2t0zLCwMLeai48TEhIif39/s+ZimZmZ5j1SDodDUVFRzR02AADwEh4TmmbMmKHdu3fr7bffbrTNZrO5LRuG0WjdxS6uaaq+JTUXmjdvnlwul/koLS29bJ8AAID38ojQNHPmTG3YsEGbN29W9+7dzfURERGS1Gimp6KiwpwVioiIUF1dnSorKy9bc+zYsUbHPX78uFvNxceprKxUfX19oxmo8+x2u4KDg90eAADg+tSuockwDM2YMUPvvvuuNm3apJ49e7pt79mzpyIiIpSbm2uuq6urU15engYOHChJio2NlZ+fn1tNWVmZSkpKzJqEhAS5XC7t2LHDrNm+fbtcLpdbTUlJicrKysyanJwc2e12xcbGtv7gAQCAV/Ftz4M/+eSTWrNmjdavX6+goCBzpsfhcCggIEA2m03p6elasGCBevXqpV69emnBggXq1KmTUlJSzNopU6Zo9uzZ6tKlizp37qyMjAz17dtXI0aMkCT17t1bo0aNUmpqqpYtWyZJmjp1qpKTkxUdHS1JSkxMVJ8+feR0OvXiiy/q5MmTysjIUGpqKjNIAACgfUPTq6++KkkaOnSo2/o33nhDkydPliTNmTNHZ86c0fTp01VZWam4uDjl5OQoKCjIrF+8eLF8fX01YcIEnTlzRsOHD9fKlSvl4+Nj1qxevVppaWnmp+zGjRunpUuXmtt9fHy0ceNGTZ8+XYMGDVJAQIBSUlL00ksvtdHoAQCAN/Go72nydnxPEwAA3scrv6cJAADAUxGaAAAALCA0AQAAWEBoAgAAsIDQBAAAYAGhCQAAwAJCEwAAgAWEJgAAAAsITQAAABYQmgAAACwgNAEAAFhAaAIAALCA0AQAAGABoQkAAMACQhMAAIAFhCYAAAALCE0AAAAWEJoAAAAsIDQBAABYQGgCAACwgNAEAABgAaEJAADAAkITAACABYQmAAAACwhNAAAAFhCaAAAALCA0AQAAWEBoAgAAsIDQBAAAYEGLQtOwYcNUVVXVaH11dbWGDRt2tX0CAADwOC0KTVu2bFFdXV2j9WfPntVnn3121Z0CAADwNL7NKd69e7f5571796q8vNxcbmhoUHZ2tv7t3/6t9XoHAADgIZoVmn74wx/KZrPJZrM1eRkuICBAr7zySqt1DgAAwFM0KzQdOnRIhmHolltu0Y4dO9S1a1dzm7+/v8LCwuTj49PqnQQAAGhvzQpNPXr0kCSdO3euTToDAADgqZoVmi7017/+VVu2bFFFRUWjEPWLX/ziqjsGAADgSVoUmpYvX64nnnhCoaGhioiIkM1mM7fZbDZCEwAAuO60KDT9+te/1vPPP6+nn366tfsDAADgkVr0PU2VlZX6yU9+0tp9AQAA8FgtCk0/+clPlJOT09p9AQAA8Fgtujx366236tlnn1VBQYH69u0rPz8/t+1paWmt0jkAAABPYTMMw2juTj179rx0gzab/va3v11Vp7xVdXW1HA6HXC6XgoODW7Xtm+dubNX2LnR44Zg2axsAAE9n9f27RTNNhw4danHHAAAAvFGL7mkCAAD4vmnRTNOjjz562e1//OMfW9QZAAAAT9Wi0FRZWem2XF9fr5KSElVVVTX5Q74AAADerkWhad26dY3WnTt3TtOnT9ctt9xy1Z0CAADwNC3+7bmLdejQQU899ZSGDh2qOXPmtFazAOAx2upTrHyCFfAOrXoj+MGDB/Xdd9+1ZpMAAAAeoUWhadasWW6Pp556Sg8//LAmTpyoiRMnWm7n008/1dixYxUZGSmbzab33nvPbfvkyZNls9ncHvHx8W41tbW1mjlzpkJDQxUYGKhx48bp6NGjbjWVlZVyOp1yOBxyOBxyOp2qqqpyqzly5IjGjh2rwMBAhYaGKi0tTXV1dc16XgAAwPWrRZfnioqK3JY7dOigrl27atGiRVf8ZN2Fampq1L9/f/3sZz/TQw891GTNqFGj9MYbb5jL/v7+btvT09P1/vvvKysrS126dNHs2bOVnJyswsJC+fj4SJJSUlJ09OhRZWdnS5KmTp0qp9Op999/X5LU0NCgMWPGqGvXrsrPz9eJEyc0adIkGYahV155xfJ4AADA9atFoWnz5s2tcvDRo0dr9OjRl62x2+2KiIhocpvL5dKKFSu0atUqjRgxQpL01ltvKSoqSh9//LGSkpK0b98+ZWdnq6CgQHFxcZKk5cuXKyEhQfv371d0dLRycnK0d+9elZaWKjIyUpK0aNEiTZ48Wc8///wlvx20trZWtbW15nJ1dXWznwMAAOAdruqepuPHjys/P1+ff/65jh8/3lp9crNlyxaFhYXptttuU2pqqioqKsxthYWFqq+vV2JiorkuMjJSMTEx2rp1qyRp27ZtcjgcZmCSpPj4eDkcDreamJgYMzBJUlJSkmpra1VYWHjJvmVmZpqX/BwOh6Kiolpt3AAAwLO0KDTV1NTo0UcfVbdu3XTvvfdq8ODBioyM1JQpU/Ttt9+2WudGjx6t1atXa9OmTVq0aJF27typYcOGmbM75eXl8vf3V0hIiNt+4eHhKi8vN2vCwsIatR0WFuZWEx4e7rY9JCRE/v7+Zk1T5s2bJ5fLZT5KS0uvarwAAMBztfhG8Ly8PL3//vuqqqpSVVWV1q9fr7y8PM2ePbvVOjdx4kSNGTNGMTExGjt2rD788EP99a9/1caNl//Yr2EYstls5vKFf76amovZ7XYFBwe7PQAAwPWpRaFp7dq1WrFihUaPHm2Ghfvvv1/Lly/Xn//859buo6lbt27q0aOHDhw4IEmKiIhQXV1do28or6ioMGeOIiIidOzYsUZtHT9+3K3m4hmlyspK1dfXN5qBAgAA308tCk3ffvttk2EiLCysVS/PXezEiRMqLS1Vt27dJEmxsbHy8/NTbm6uWVNWVqaSkhINHDhQkpSQkCCXy6UdO3aYNdu3b5fL5XKrKSkpUVlZmVmTk5Mju92u2NjYNhsPAADwHi0KTQkJCfrlL3+ps2fPmuvOnDmj5557TgkJCZbbOX36tIqLi1VcXCxJOnTokIqLi3XkyBGdPn1aGRkZ2rZtmw4fPqwtW7Zo7NixCg0N1Y9//GNJksPh0JQpUzR79mx98sknKioq0k9/+lP17dvX/DRd7969NWrUKKWmpqqgoEAFBQVKTU1VcnKyoqOjJUmJiYnq06ePnE6nioqK9MknnygjI0OpqalccgMAAJJa+JUDS5Ys0ejRo9W9e3f1799fNptNxcXFstvtysnJsdzOrl27dN9995nLs2bNkiRNmjRJr776qr744gv96U9/UlVVlbp166b77rtP77zzjoKCgsx9Fi9eLF9fX02YMEFnzpzR8OHDtXLlSvM7miRp9erVSktLMz9lN27cOC1dutTc7uPjo40bN2r69OkaNGiQAgIClJKSopdeeqklTw8AALgO2QzDMFqy45kzZ/TWW2/pyy+/lGEY6tOnj/793/9dAQEBrd1Hr1FdXS2HwyGXy9XqM1Rt9ZtXEr97BVjFb88B1yer798tmmnKzMxUeHi4UlNT3db/8Y9/1PHjx/X000+3pFkAAACP1aJ7mpYtW6bbb7+90fo77rhDr7322lV3CgAAwNO0KDSVl5ebn2C7UNeuXd0+gQYAAHC9aFFoioqK0ueff95o/eeff+72UyQAAADXixbd0/TYY48pPT1d9fX1GjZsmCTpk08+0Zw5c1r1G8EBAAA8RYtC05w5c3Ty5ElNnz5ddXV1kqSOHTvq6aef1rx581q1gwAAAJ6gRaHJZrPpN7/5jZ599lnt27dPAQEB6tWrl+x2e2v3DwAAwCO0KDSdd8MNN+juu+9urb4AAAB4rBbdCA4AAPB9Q2gCAACwgNAEAABgwVXd0wQAnqYtf6cRwPcbM00AAAAWEJoAAAAsIDQBAABYQGgCAACwgNAEAABgAaEJAADAAkITAACABYQmAAAACwhNAAAAFhCaAAAALCA0AQAAWEBoAgAAsIDQBAAAYAGhCQAAwAJCEwAAgAWEJgAAAAsITQAAABYQmgAAACwgNAEAAFhAaAIAALCA0AQAAGABoQkAAMACQhMAAIAFhCYAAAALCE0AAAAWEJoAAAAsIDQBAABYQGgCAACwgNAEAABgAaEJAADAAkITAACABYQmAAAACwhNAAAAFhCaAAAALCA0AQAAWEBoAgAAsKBdQ9Onn36qsWPHKjIyUjabTe+9957bdsMwNH/+fEVGRiogIEBDhw7Vnj173Gpqa2s1c+ZMhYaGKjAwUOPGjdPRo0fdaiorK+V0OuVwOORwOOR0OlVVVeVWc+TIEY0dO1aBgYEKDQ1VWlqa6urq2mLYAADAC7VraKqpqVH//v21dOnSJre/8MILevnll7V06VLt3LlTERERGjlypE6dOmXWpKena926dcrKylJ+fr5Onz6t5ORkNTQ0mDUpKSkqLi5Wdna2srOzVVxcLKfTaW5vaGjQmDFjVFNTo/z8fGVlZWnt2rWaPXt22w0eAAB4Fd/2PPjo0aM1evToJrcZhqElS5bomWee0YMPPihJevPNNxUeHq41a9Zo2rRpcrlcWrFihVatWqURI0ZIkt566y1FRUXp448/VlJSkvbt26fs7GwVFBQoLi5OkrR8+XIlJCRo//79io6OVk5Ojvbu3avS0lJFRkZKkhYtWqTJkyfr+eefV3Bw8DV4NgAAgCfz2HuaDh06pPLyciUmJprr7Ha7hgwZoq1bt0qSCgsLVV9f71YTGRmpmJgYs2bbtm1yOBxmYJKk+Ph4ORwOt5qYmBgzMElSUlKSamtrVVhYeMk+1tbWqrq62u0BAACuTx4bmsrLyyVJ4eHhbuvDw8PNbeXl5fL391dISMhla8LCwhq1HxYW5lZz8XFCQkLk7+9v1jQlMzPTvE/K4XAoKiqqmaMEAADewmND03k2m81t2TCMRusudnFNU/UtqbnYvHnz5HK5zEdpaell+wUAALyXx4amiIgISWo001NRUWHOCkVERKiurk6VlZWXrTl27Fij9o8fP+5Wc/FxKisrVV9f32gG6kJ2u13BwcFuDwAAcH3y2NDUs2dPRUREKDc311xXV1envLw8DRw4UJIUGxsrPz8/t5qysjKVlJSYNQkJCXK5XNqxY4dZs337drlcLreakpISlZWVmTU5OTmy2+2KjY1t03ECAADv0K6fnjt9+rS++uorc/nQoUMqLi5W586dddNNNyk9PV0LFixQr1691KtXLy1YsECdOnVSSkqKJMnhcGjKlCmaPXu2unTpos6dOysjI0N9+/Y1P03Xu3dvjRo1SqmpqVq2bJkkaerUqUpOTlZ0dLQkKTExUX369JHT6dSLL76okydPKiMjQ6mpqcweAQAASe0cmnbt2qX77rvPXJ41a5YkadKkSVq5cqXmzJmjM2fOaPr06aqsrFRcXJxycnIUFBRk7rN48WL5+vpqwoQJOnPmjIYPH66VK1fKx8fHrFm9erXS0tLMT9mNGzfO7buhfHx8tHHjRk2fPl2DBg1SQECAUlJS9NJLL7X1UwAAALyEzTAMo707cb2orq6Ww+GQy+Vq9Rmqm+dubNX2LnR44Zg2axu41tryXGkrnINA+7L6/u2x9zQBAAB4EkITAACABYQmAAAAC9r1RnAAAPcsAt6CmSYAAAALCE0AAAAWEJoAAAAsIDQBAABYQGgCAACwgNAEAABgAaEJAADAAkITAACABYQmAAAACwhNAAAAFhCaAAAALCA0AQAAWEBoAgAAsIDQBAAAYAGhCQAAwAJCEwAAgAWEJgAAAAsITQAAABYQmgAAACzwbe8OAPh+unnuxvbuAgA0CzNNAAAAFhCaAAAALCA0AQAAWEBoAgAAsIDQBAAAYAGhCQAAwAJCEwAAgAWEJgAAAAsITQAAABYQmgAAACwgNAEAAFhAaAIAALCA0AQAAGABoQkAAMACQhMAAIAFhCYAAAALCE0AAAAWEJoAAAAsIDQBAABYQGgCAACwgNAEAABgAaEJAADAAkITAACABYQmAAAACwhNAAAAFnh0aJo/f75sNpvbIyIiwtxuGIbmz5+vyMhIBQQEaOjQodqzZ49bG7W1tZo5c6ZCQ0MVGBiocePG6ejRo241lZWVcjqdcjgccjgccjqdqqqquhZDBAAAXsKjQ5Mk3XHHHSorKzMfX3zxhbnthRde0Msvv6ylS5dq586dioiI0MiRI3Xq1CmzJj09XevWrVNWVpby8/N1+vRpJScnq6GhwaxJSUlRcXGxsrOzlZ2dreLiYjmdzms6TgAA4Nl827sDV+Lr6+s2u3SeYRhasmSJnnnmGT344IOSpDfffFPh4eFas2aNpk2bJpfLpRUrVmjVqlUaMWKEJOmtt95SVFSUPv74YyUlJWnfvn3Kzs5WQUGB4uLiJEnLly9XQkKC9u/fr+jo6Ev2rba2VrW1teZydXV1aw4dAAB4EI+faTpw4IAiIyPVs2dPPfzww/rb3/4mSTp06JDKy8uVmJho1trtdg0ZMkRbt26VJBUWFqq+vt6tJjIyUjExMWbNtm3b5HA4zMAkSfHx8XI4HGbNpWRmZpqX9BwOh6Kiolpt3AAAwLN4dGiKi4vTn/70J3300Udavny5ysvLNXDgQJ04cULl5eWSpPDwcLd9wsPDzW3l5eXy9/dXSEjIZWvCwsIaHTssLMysuZR58+bJ5XKZj9LS0haPFQAAeDaPvjw3evRo8899+/ZVQkKCfvCDH+jNN99UfHy8JMlms7ntYxhGo3UXu7imqXor7djtdtnt9iuOAwAAeD+Pnmm6WGBgoPr27asDBw6Y9zldPBtUUVFhzj5FRESorq5OlZWVl605duxYo2MdP3680SwWAAD4/vKq0FRbW6t9+/apW7du6tmzpyIiIpSbm2tur6urU15engYOHChJio2NlZ+fn1tNWVmZSkpKzJqEhAS5XC7t2LHDrNm+fbtcLpdZAwAA4NGX5zIyMjR27FjddNNNqqio0K9//WtVV1dr0qRJstlsSk9P14IFC9SrVy/16tVLCxYsUKdOnZSSkiJJcjgcmjJlimbPnq0uXbqoc+fOysjIUN++fc1P0/Xu3VujRo1Samqqli1bJkmaOnWqkpOTL/vJOQAA8P3i0aHp6NGjeuSRR/TNN9+oa9euio+PV0FBgXr06CFJmjNnjs6cOaPp06ersrJScXFxysnJUVBQkNnG4sWL5evrqwkTJujMmTMaPny4Vq5cKR8fH7Nm9erVSktLMz9lN27cOC1duvTaDhYAAHg0m2EYRnt34npRXV0th8Mhl8ul4ODgVm375rkbW7W9Cx1eOKbN2gYupS3/TuP/4/wGrszq+7dX3dMEAADQXjz68hyA9sVsEAD8f8w0AQAAWEBoAgAAsIDQBAAAYAGhCQAAwAJCEwAAgAWEJgAAAAsITQAAABYQmgAAACwgNAEAAFhAaAIAALCA0AQAAGABoQkAAMACQhMAAIAFhCYAAAALCE0AAAAWEJoAAAAsIDQBAABY4NveHQAAtJ2b525sk3YPLxzTJu0CnozQBP5RBQDAAi7PAQAAWEBoAgAAsIDLc4CXa6vLqwAAd4Qm4Boh3ACAd+PyHAAAgAWEJgAAAAu4PIc205aXo/g6AwDAtcZMEwAAgAXMNAEX4GZtAMClEJrglQg3AIBrjctzAAAAFhCaAAAALCA0AQAAWEBoAgAAsIDQBAAAYAGfngMANBtfXovvI2aaAAAALGCmCQDgUdpqFosZLFwtZpoAAAAsIDQBAABYwOU5AMD3Ajev42ox0wQAAGABM00AAFwlbl7/fmCmCQAAwAJCEwAAgAWEJgAAAAsITQAAABZwI/hFfv/73+vFF19UWVmZ7rjjDi1ZskSDBw9u724BAL6H+JoEz8JM0wXeeecdpaen65lnnlFRUZEGDx6s0aNH68iRI+3dNQAA0M5shmEY7d0JTxEXF6cBAwbo1VdfNdf17t1b48ePV2Zm5hX3r66ulsPhkMvlUnBwcKv2rS3/twEAQGvytlksq+/fXJ77l7q6OhUWFmru3Llu6xMTE7V169Ym96mtrVVtba257HK5JP3zyW9t52q/bfU2AQBoCzc99T9t0m7Jc0lt0u759+0rzSMRmv7lm2++UUNDg8LDw93Wh4eHq7y8vMl9MjMz9dxzzzVaHxUV1SZ9BADg+8yxpG3bP3XqlBwOxyW3E5ouYrPZ3JYNw2i07rx58+Zp1qxZ5vK5c+d08uRJdenS5ZL7tER1dbWioqJUWlra6pf9PMX1PkbG5/2u9zFe7+OTrv8xMr6WMwxDp06dUmRk5GXrCE3/EhoaKh8fn0azShUVFY1mn86z2+2y2+1u62688ca26qKCg4OvyxPhQtf7GBmf97vex3i9j0+6/sfI+FrmcjNM5/HpuX/x9/dXbGyscnNz3dbn5uZq4MCB7dQrAADgKZhpusCsWbPkdDp11113KSEhQa+//rqOHDmixx9/vL27BgAA2hmh6QITJ07UiRMn9Ktf/UplZWWKiYnRBx98oB49erRrv+x2u375y182uhR4Pbnex8j4vN/1PsbrfXzS9T9Gxtf2+J4mAAAAC7inCQAAwAJCEwAAgAWEJgAAAAsITQAAABYQmtrJ73//e/Xs2VMdO3ZUbGysPvvss8vW5+XlKTY2Vh07dtQtt9yi1157rVHN2rVr1adPH9ntdvXp00fr1q1rq+5fUXPG9+6772rkyJHq2rWrgoODlZCQoI8++sitZuXKlbLZbI0eZ8+ebeuhNKk549uyZUuTff/yyy/d6jzp9ZOaN8bJkyc3OcY77rjDrPGk1/DTTz/V2LFjFRkZKZvNpvfee++K+3jTOdjc8XnjOdjcMXrbedjc8XnbOZiZmam7775bQUFBCgsL0/jx47V///4r7tfe5yGhqR288847Sk9P1zPPPKOioiINHjxYo0eP1pEjR5qsP3TokO6//34NHjxYRUVF+vnPf660tDStXbvWrNm2bZsmTpwop9Op//u//5PT6dSECRO0ffv2azUsU3PH9+mnn2rkyJH64IMPVFhYqPvuu09jx45VUVGRW11wcLDKysrcHh07drwWQ3LT3PGdt3//fre+9+rVy9zmSa+f1Pwx/va3v3UbW2lpqTp37qyf/OQnbnWe8hrW1NSof//+Wrp0qaV6bzsHmzs+bzsHpeaP8TxvOQ+bOz5vOwfz8vL05JNPqqCgQLm5ufruu++UmJiompqaS+7jEeehgWvuRz/6kfH444+7rbv99tuNuXPnNlk/Z84c4/bbb3dbN23aNCM+Pt5cnjBhgjFq1Ci3mqSkJOPhhx9upV5b19zxNaVPnz7Gc889Zy6/8cYbhsPhaK0uXpXmjm/z5s2GJKOysvKSbXrS62cYV/8arlu3zrDZbMbhw4fNdZ70Gl5IkrFu3brL1njbOXghK+NriiefgxezMkZvPA/Pa8lr6E3noGEYRkVFhSHJyMvLu2SNJ5yHzDRdY3V1dSosLFRiYqLb+sTERG3durXJfbZt29aoPikpSbt27VJ9ff1lay7VZltpyfgudu7cOZ06dUqdO3d2W3/69Gn16NFD3bt3V3JycqP/BV8LVzO+O++8U926ddPw4cO1efNmt22e8vpJrfMarlixQiNGjGj0xbCe8Bq2hDedg63Bk8/Bq+Ut5+HV8rZz0OVySVKjv3MX8oTzkNB0jX3zzTdqaGho9CPA4eHhjX4s+Lzy8vIm67/77jt98803l625VJttpSXju9iiRYtUU1OjCRMmmOtuv/12rVy5Uhs2bNDbb7+tjh07atCgQTpw4ECr9v9KWjK+bt266fXXX9fatWv17rvvKjo6WsOHD9enn35q1njK6ydd/WtYVlamDz/8UI899pjbek95DVvCm87B1uDJ52BLedt5eDW87Rw0DEOzZs3SPffco5iYmEvWecJ5yM+otBObzea2bBhGo3VXqr94fXPbbEst7cvbb7+t+fPna/369QoLCzPXx8fHKz4+3lweNGiQBgwYoFdeeUX/9V//1Xodt6g544uOjlZ0dLS5nJCQoNLSUr300ku69957W9TmtdDS/qxcuVI33nijxo8f77be017D5vK2c7ClvOUcbC5vPQ9bwtvOwRkzZmj37t3Kz8+/Ym17n4fMNF1joaGh8vHxaZR6KyoqGqXj8yIiIpqs9/X1VZcuXS5bc6k220pLxnfeO++8oylTpui///u/NWLEiMvWdujQQXffffc1/x/S1YzvQvHx8W5995TXT7q6MRqGoT/+8Y9yOp3y9/e/bG17vYYt4U3n4NXwhnOwNXnyedhS3nYOzpw5Uxs2bNDmzZvVvXv3y9Z6wnlIaLrG/P39FRsbq9zcXLf1ubm5GjhwYJP7JCQkNKrPycnRXXfdJT8/v8vWXKrNttKS8Un//N/t5MmTtWbNGo0ZM+aKxzEMQ8XFxerWrdtV97k5Wjq+ixUVFbn13VNeP+nqxpiXl6evvvpKU6ZMueJx2us1bAlvOgdbylvOwdbkyedhS3nLOWgYhmbMmKF3331XmzZtUs+ePa+4j0ech61yOzmaJSsry/Dz8zNWrFhh7N2710hPTzcCAwPNTznMnTvXcDqdZv3f/vY3o1OnTsZTTz1l7N2711ixYoXh5+dn/PnPfzZrPv/8c8PHx8dYuHChsW/fPmPhwoWGr6+vUVBQ4PHjW7NmjeHr62v87ne/M8rKysxHVVWVWTN//nwjOzvbOHjwoFFUVGT87Gc/M3x9fY3t27d7/PgWL15srFu3zvjrX/9qlJSUGHPnzjUkGWvXrjVrPOn1M4zmj/G8n/70p0ZcXFyTbXrSa3jq1CmjqKjIKCoqMiQZL7/8slFUVGT8/e9/NwzD+8/B5o7P285Bw2j+GL3tPGzu+M7zlnPwiSeeMBwOh7Flyxa3v3PffvutWeOJ5yGhqZ387ne/M3r06GH4+/sbAwYMcPuY5aRJk4whQ4a41W/ZssW48847DX9/f+Pmm282Xn311UZt/s///I8RHR1t+Pn5GbfffrvbPwbXWnPGN2TIEENSo8ekSZPMmvT0dOOmm24y/P39ja5duxqJiYnG1q1br+GI3DVnfL/5zW+MH/zgB0bHjh2NkJAQ45577jE2btzYqE1Pev0Mo/l/R6uqqoyAgADj9ddfb7I9T3oNz3/8/FJ/57z9HGzu+LzxHGzuGL3tPGzJ31FvOgebGpsk44033jBrPPE8tP2r8wAAALgM7mkCAACwgNAEAABgAaEJAADAAkITAACABYQmAAAACwhNAAAAFhCaAAAALCA0AQAAWEBoAuBVhg4dqvT09Ktq4/Dhw7LZbCouLm6VPrW3LVu2yGazqaqqyvI+N998s5YsWdJmfQKuR4QmANe1yZMna/z48W7roqKiVFZWppiYmKtq++9//7vsdruqq6uvqh0A3sG3vTsAANeaj4+PIiIirrqd9evXa+jQoQoODm6FXgHwdMw0AWgV2dnZuueee3TjjTeqS5cuSk5O1sGDB83t5y+Jvfvuu7rvvvvUqVMn9e/fX9u2bTNrTpw4oUceeUTdu3dXp06d1LdvX7399tuXPOavfvUr9e3bt9H62NhY/eIXv9D8+fP15ptvav369bLZbLLZbNqyZUuTl+f27NmjMWPGKDg4WEFBQRo8eLBb/5uyfv16jRs3rslt5y+ZffTRR7rzzjsVEBCgYcOGqaKiQh9++KF69+6t4OBgPfLII/r222/N/Wpra5WWlqawsDB17NhR99xzj3bu3OnW9gcffKDbbrtNAQEBuu+++3T48OFGx9+6davuvfdeBQQEKCoqSmlpaaqpqbnseABcHqEJQKuoqanRrFmztHPnTn3yySfq0KGDfvzjH+vcuXNudc8884wyMjJUXFys2267TY888oi+++47SdLZs2cVGxur//3f/1VJSYmmTp0qp9Op7du3N3nMRx99VHv37nULFbt371ZRUZEmT56sjIwMTZgwQaNGjVJZWZnKyso0cODARu18/fXXuvfee9WxY0dt2rRJhYWFevTRR81+NaWqqkqfffbZJUPTefPnz9fSpUu1detWlZaWasKECVqyZInWrFmjjRs3Kjc3V6+88opZP2fOHK1du1Zvvvmm/vKXv+jWW29VUlKSTp48KUkqLS3Vgw8+qPvvv1/FxcV67LHHNHfuXLdjfvHFF0pKStKDDz6o3bt365133lF+fr5mzJhx2b4CuAIDANpARUWFIcn44osvDMMwjEOHDhmSjD/84Q9mzZ49ewxJxr59+y7Zzv3332/Mnj3bXB4yZIjxH//xH+by6NGjjSeeeMJcTk9PN4YOHWouT5o0yXjggQfc2jzfl6KiIsMwDGPevHlGz549jbq6OsvjW716tTFgwIBLbt+8ebMhyfj444/NdZmZmYYk4+DBg+a6adOmGUlJSYZhGMbp06cNPz8/Y/Xq1eb2uro6IzIy0njhhRfMvvbu3ds4d+6cWfP0008bkozKykrDMAzD6XQaU6dOdevPZ599ZnTo0ME4c+aMYRiG0aNHD2Px4sWWxwvAMJhpAtAqDh48qJSUFN1yyy0KDg5Wz549JUlHjhxxq+vXr5/5527dukmSKioqJEkNDQ16/vnn1a9fP3Xp0kU33HCDcnJyGrVxodTUVL399ts6e/as6uvrtXr1aj366KPN6ntxcbEGDx4sPz8/y/tc7tLchS4cb3h4uDp16qRbbrnFbd358R88eFD19fUaNGiQud3Pz08/+tGPtG/fPknSvn37FB8fL5vNZtYkJCS4HbOwsFArV67UDTfcYD6SkpJ07tw5HTp0yPIYAbjjRnAArWLs2LGKiorS8uXLFRkZqXPnzikmJkZ1dXVudRcGk/Nv/Ocv4S1atEiLFy/WkiVL1LdvXwUGBio9Pb1RGxcf1263a926dbLb7aqtrdVDDz3UrL4HBAQ0q76+vl7Z2dmaN2/eFWsvHu/Fwcxms5njNwzDXHchwzDMdedrLufcuXOaNm2a0tLSGm276aabrrg/gKYRmgBctRMnTmjfvn1atmyZBg8eLEnKz89vdjufffaZHnjgAf30pz+V9M83/wMHDqh3796X3MfX11eTJk3SG2+8IbvdrocfflidOnUyt/v7+6uhoeGyx+3Xr5/efPNN1dfXW5pt2rx5s2688Ub98Ic/tDYwi2699Vb5+/srPz9fKSkpkv4Z0Hbt2mV+N1WfPn303nvvue1XUFDgtjxgwADt2bNHt956a6v2D/i+4/IcgKsWEhKiLl266PXXX9dXX32lTZs2adasWc1u59Zbb1Vubq62bt2qffv2adq0aSovL7/ifo899pg2bdqkDz/8sNGluZtvvlm7d+/W/v379c0336i+vr7R/jNmzFB1dbUefvhh7dq1SwcOHNCqVau0f//+Jo+3YcMGS5fmmiswMFBPPPGE/vM//1PZ2dnau3evUlNT9e2332rKlCmSpMcff1wHDx7UrFmztH//fq1Zs0YrV650a+fpp5/Wtm3b9OSTT6q4uFgHDhzQhg0bNHPmzFbvM/B9QmgCcNU6dOigrKwsFRYWKiYmRk899ZRefPHFZrfz7LPPasCAAUpKStLQoUMVERHR6Ispm9KrVy8NHDhQ0dHRiouLc9uWmpqq6Oho3XXXXeratas+//zzRvt36dJFmzZt0unTpzVkyBDFxsZq+fLll5x12rBhgx544IFmj8+KhQsX6qGHHpLT6dSAAQP01Vdf6aOPPlJISIikf15eW7t2rd5//331799fr732mhYsWODWRr9+/ZSXl6cDBw5o8ODBuvPOO/Xss8+a95ABaBmbYeUCOQB4MMMwdPvtt2vatGktmuFqjr/85S8aNmyYjh8/3qwbxwF4P+5pAuDVKioqtGrVKn399df62c9+1ubH++677/TKK68QmIDvIWaaAHg1m82m0NBQ/fa3vzVvngaAtsBMEwCvxv/7AFwr3AgOAABgAaEJAADAAkITAACABYQmAAAACwhNAAAAFhCaAAAALCA0AQAAWEBoAgAAsOD/AYbm7ZFE9++RAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(ratio, bins=20)\n",
    "plt.xlabel('analytic / model ')\n",
    "plt.ylabel('count')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fb9311d-ab45-417a-9c06-819f8ab4662b",
   "metadata": {},
   "source": [
    "### Reweight reference distribution to data distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "8fa5af69-b1d8-450d-b9ce-df247158e0ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "WS_analytic = (mu * pS_over_pB + 1 - mu)  / (mu * pS_over_pB + 2 - 2 * mu)\n",
    "WS_model = (mu * likelihood + 1 - mu)  / (mu * likelihood + 2 - 2 * mu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "ecee69ec-5656-496e-beb5-0236824a671b",
   "metadata": {},
   "outputs": [],
   "source": [
    "rw_analytic = WS_analytic / (1 - WS_analytic)\n",
    "rw_model = WS_model / (1 - WS_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "e6232e22-3b30-4d04-bd84-ed9f4dc806f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Fraction of Events')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(D[:, 0], bins=40, range=(0, 20), alpha=0.6, label='Data', histtype='step', density=True)\n",
    "plt.hist(R[:, 0], weights=rw_analytic, bins=40, range=(0, 20), alpha=0.6, label='Reference Reweight from Analytic', histtype='step', density=True)\n",
    "plt.hist(R[:, 0], weights=rw_model, bins=40, range=(0, 20), alpha=0.6, label='Reference Reweight from Model', histtype='step', density=True)\n",
    "plt.hist(R[:, 0], bins=40, range=(0, 20), alpha=0.6, label='Reference', histtype='step', color='r', density=True)\n",
    "plt.legend()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Fraction of Events')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c4f67fd-0690-4242-9236-29a253685017",
   "metadata": {},
   "source": [
    "### Train for mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "fb4555cf-e163-4b17-a5cf-e82ffb16d4e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "from tensorflow.keras import Input, Model\n",
    "from tensorflow.keras.layers import Dense\n",
    "\n",
    "class MinMaxRegularizer(tf.keras.regularizers.Regularizer):\n",
    "  def __init__(self, min_val, max_val, l=1.0):\n",
    "      self.min_val = min_val\n",
    "      self.max_val = max_val\n",
    "      self.l = l\n",
    "\n",
    "  def __call__(self, x):\n",
    "      x_under = tf.cast(tf.less(x, self.min_val), dtype=tf.float32)\n",
    "      x_over  = tf.cast(tf.greater(x, self.max_val), dtype=tf.float32)\n",
    "      under_penalty = (tf.exp(self.min_val - x) - 1)\n",
    "      over_penalty = (tf.exp(x - self.max_val) - 1)\n",
    "      penalty = self.l * tf.math.reduce_sum(((x_under * under_penalty) + (x_over * over_penalty)))\n",
    "      return penalty\n",
    "\n",
    "  def get_config(self):\n",
    "      return {'l': float(self.l),\n",
    "              'min_val': float(self.min_val),\n",
    "              'max_val': float(self.max_val)}\n",
    "\n",
    "def get_single_parameter_model(default,\n",
    "                               name = None,\n",
    "                               exponential=False,\n",
    "                               regularizer=None):\n",
    "    inputs = Input(shape=(1,))\n",
    "    outputs = Dense(1, use_bias=False,\n",
    "                    kernel_initializer=tf.constant_initializer(float(default)),\n",
    "                    kernel_regularizer=regularizer,\n",
    "                    activation='linear',\n",
    "                    name=name)(inputs)\n",
    "    if exponential:\n",
    "        outputs = tf.exp(outputs)\n",
    "    return Model(inputs=inputs, outputs=outputs)\n",
    "\n",
    "def create_ws_model(fs_model, feature_dim, kappa=1.0):\n",
    "    x = Input(shape=(feature_dim,))\n",
    "    fs_out = fs_model(x)\n",
    "    mu_input = get_single_parameter_model(-4., name='mu',\n",
    "                                          exponential=True,\n",
    "                                          regularizer=MinMaxRegularizer(-10.0, 0.0),)\n",
    "    mu_out = mu_input(tf.ones_like(x)[:, :1])\n",
    "    LLR = fs_out / (1 - fs_out + 1e-5)\n",
    "    if kappa == 'trainable':\n",
    "        kappa_input = get_single_parameter_model(5., name='kappa',\n",
    "                                                 exponential=False,\n",
    "                                                 regularizer=MinMaxRegularizer(1, 30))\n",
    "        kappa = kappa_input(tf.ones_like(x)[:, :1])\n",
    "    LLR_xs = 1. + mu_out * (LLR * kappa - 1.)\n",
    "    ws_out = LLR_xs / (LLR_xs + 1 - mu_out )\n",
    "    ws_model = tf.keras.Model(inputs=x, outputs=ws_out, name='SemiWeakly')\n",
    "    return ws_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "5d91eb65-99af-4cee-980c-970b57fd0ce6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Craete weakly datasets\n",
    "\n",
    "S_test = X_test[y_test == 1]\n",
    "B_test = X_test[y_test == 0]\n",
    "\n",
    "N_B = 100000\n",
    "mu = 0.01\n",
    "N_S = int(mu / (1 - mu) * N_B)\n",
    "\n",
    "D = np.concatenate([S_test[:N_S], B_test[:N_B]], axis=0)\n",
    "R = B_test[N_B : 2 * N_B]\n",
    "\n",
    "X = np.concatenate([D, R])\n",
    "Y = np.concatenate([np.ones(D.shape[0]), np.zeros(R.shape[0])])\n",
    "\n",
    "x_train, x_val, y_train, y_val = train_test_split(X, Y, test_size=0.5, random_state=2024)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "62be0369-472c-47c4-b330-dd1dfc29434e",
   "metadata": {},
   "outputs": [],
   "source": [
    "for layer in model.layers:\n",
    "    layer.trainable = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "44cb58a7-e6cd-450b-8a05-0c5252f22958",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "ws_model = create_ws_model(model, feature_dim=2, kappa=kappa)\n",
    "ws_model.compile(optimizer='adam', loss='binary_crossentropy', metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "71bfcea9-1e7f-48b2-b703-121203fea1f6",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/1000\n",
      "99/99 [==============================] - 1s 3ms/step - loss: 0.6931 - accuracy: 0.5015 - val_loss: 0.6932 - val_accuracy: 0.5022\n",
      "Epoch 2/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5011 - val_loss: 0.6932 - val_accuracy: 0.5022\n",
      "Epoch 3/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5014 - val_loss: 0.6932 - val_accuracy: 0.5015\n",
      "Epoch 4/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.4999 - val_loss: 0.6931 - val_accuracy: 0.5017\n",
      "Epoch 5/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5020 - val_loss: 0.6931 - val_accuracy: 0.5013\n",
      "Epoch 6/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5021 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 7/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5017 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 8/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5016 - val_loss: 0.6931 - val_accuracy: 0.5020\n",
      "Epoch 9/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5019 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 10/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5011 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 11/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5007 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 12/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5016 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 13/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5017 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 14/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5016 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 15/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5019 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 16/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5000 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 17/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5007 - val_loss: 0.6931 - val_accuracy: 0.5013\n",
      "Epoch 18/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5005 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 19/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5016 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 20/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5017 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 21/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5011 - val_loss: 0.6931 - val_accuracy: 0.5014\n",
      "Epoch 22/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5013 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 23/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5013 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 24/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5014 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 25/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5011 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 26/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5004 - val_loss: 0.6931 - val_accuracy: 0.5016\n",
      "Epoch 27/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5009 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 28/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5014 - val_loss: 0.6931 - val_accuracy: 0.5019\n",
      "Epoch 29/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5008 - val_loss: 0.6931 - val_accuracy: 0.5023\n",
      "Epoch 30/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5014 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 31/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5012 - val_loss: 0.6931 - val_accuracy: 0.5023\n",
      "Epoch 32/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5016 - val_loss: 0.6931 - val_accuracy: 0.5018\n",
      "Epoch 33/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5009 - val_loss: 0.6931 - val_accuracy: 0.5014\n",
      "Epoch 34/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5005 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 35/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5007 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 36/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5014 - val_loss: 0.6931 - val_accuracy: 0.5014\n",
      "Epoch 37/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5004 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 38/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5013 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 39/1000\n",
      "99/99 [==============================] - 0s 3ms/step - loss: 0.6931 - accuracy: 0.5005 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 40/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5007 - val_loss: 0.6931 - val_accuracy: 0.5018\n",
      "Epoch 41/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5027 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 42/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5004 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 43/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5006 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 44/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5009 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 45/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5006 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 46/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5013 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 47/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5018 - val_loss: 0.6931 - val_accuracy: 0.5018\n",
      "Epoch 48/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5013 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 49/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5011 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 50/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5009 - val_loss: 0.6931 - val_accuracy: 0.5013\n",
      "Epoch 51/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5012 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 52/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5011 - val_loss: 0.6931 - val_accuracy: 0.5014\n",
      "Epoch 53/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5004 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 54/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5004 - val_loss: 0.6931 - val_accuracy: 0.5017\n",
      "Epoch 55/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5007 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 56/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5012 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 57/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5013 - val_loss: 0.6931 - val_accuracy: 0.5017\n",
      "Epoch 58/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5001 - val_loss: 0.6931 - val_accuracy: 0.5020\n",
      "Epoch 59/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5010 - val_loss: 0.6931 - val_accuracy: 0.5023\n",
      "Epoch 60/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5005 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 61/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5000 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 62/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5017 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 63/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5007 - val_loss: 0.6931 - val_accuracy: 0.5018\n",
      "Epoch 64/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5010 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 65/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5010 - val_loss: 0.6931 - val_accuracy: 0.5016\n",
      "Epoch 66/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5008 - val_loss: 0.6931 - val_accuracy: 0.5020\n",
      "Epoch 67/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5008 - val_loss: 0.6931 - val_accuracy: 0.5023\n",
      "Epoch 68/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5004 - val_loss: 0.6931 - val_accuracy: 0.5014\n",
      "Epoch 69/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5009 - val_loss: 0.6931 - val_accuracy: 0.5023\n",
      "Epoch 70/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5010 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 71/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5008 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 72/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5013 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 73/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5001 - val_loss: 0.6931 - val_accuracy: 0.5023\n",
      "Epoch 74/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5010 - val_loss: 0.6931 - val_accuracy: 0.5020\n",
      "Epoch 75/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5010 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 76/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5008 - val_loss: 0.6931 - val_accuracy: 0.5022\n",
      "Epoch 77/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5008 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 78/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5013 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 79/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5013 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 80/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5007 - val_loss: 0.6931 - val_accuracy: 0.5015\n",
      "Epoch 81/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5015 - val_loss: 0.6931 - val_accuracy: 0.5020\n",
      "Epoch 82/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5002 - val_loss: 0.6931 - val_accuracy: 0.5021\n",
      "Epoch 83/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5009 - val_loss: 0.6931 - val_accuracy: 0.5023\n",
      "Epoch 84/1000\n",
      "99/99 [==============================] - 0s 2ms/step - loss: 0.6931 - accuracy: 0.5003 - val_loss: 0.6931 - val_accuracy: 0.5015\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.src.callbacks.History at 0x7fc937555610>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "early_stopping = tf.keras.callbacks.EarlyStopping(\n",
    "    monitor='val_loss',  \n",
    "    patience=10,        \n",
    "    restore_best_weights=True\n",
    ")\n",
    "\n",
    "ws_model.fit(x_train, y_train,\n",
    "             validation_data=(x_val, y_val),\n",
    "             epochs=1000,\n",
    "             batch_size=1024,\n",
    "             callbacks=[early_stopping])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "bc5c62ca-2c6d-4c96-be0d-e4aa0a8ba30f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3141/3141 [==============================] - 2s 566us/step - loss: 0.6931 - accuracy: 0.5007\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0.6930612325668335, 0.5007014870643616]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ws_model.evaluate(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "606379ba-6bd2-4c02-a77a-b14aa5508423",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted mu: 0.010450861416757107\n",
      "truth mu: 0.01\n"
     ]
    }
   ],
   "source": [
    "weights = {}\n",
    "for weight in ws_model.trainable_weights:\n",
    "    name = weight.name.split('/')[0]\n",
    "    weights[name] = weight[0][0]\n",
    "print(f'predicted mu: {np.exp(weights[\"mu\"])}')\n",
    "print(f'truth mu: {mu}')"
   ]
  }
 ],
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