FL005_remote_replay.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# `FL005_remote_replay` (Frank lab data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\etien\\Anaconda3\\lib\\site-packages\\matplotlib\\cbook\\deprecation.py:106: MatplotlibDeprecationWarning: The mpl_toolkits.axes_grid module was deprecated in version 2.1. Use mpl_toolkits.axes_grid1 and mpl_toolkits.axisartist provies the same functionality instead.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Etienne Ackermann, Sun Dec 03 2017 16:51:58 \n",
      "\n",
      "CPython 3.6.3\n",
      "IPython 6.1.0\n",
      "\n",
      "nelpy 0.1.1\n",
      "numpy 1.12.1\n",
      "scipy 0.19.1\n",
      "pandas 0.21.0\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -a \"Etienne Ackermann,\" -n -t -v -p nelpy,numpy,scipy,pandas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Overview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, I mainly implement Mattias' regression analysis, to determine [quantitatively] which events are considered significant replay, both local and remote.\n",
    "\n",
    "Mattias used N=10,000 shuffles to compute significance, and I **think** he did this on the linearized positions? Yes, he did indeed. What is still unclear though, is how he decided when to use center-outer ordering and when to use outer-outer ordering? I suppose I will compute both, and use the one with the highest p-value as the event's p-value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import warnings\n",
    "\n",
    "import nelpy as nel\n",
    "import nelpy.io\n",
    "import nelpy.plotting as npl\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fileroot = '../../../../neoReader/' \n",
    "infile = 'FrankLabData-BonConFra-no-eeg03b.nel' # saved with Pandas=0.21\n",
    "outfile = 'FrankLabData-BonConFra-no-eeg05b.nel' # saved with Pandas=0.21\n",
    "# FrankLabData = nel.load_pkl(fileroot + infile) \n",
    "FrankLabData = nel.load_pkl(fileroot + outfile) \n",
    "\n",
    "data = FrankLabData.data\n",
    "sessions = FrankLabData.sessions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
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uuTqvSdoG2Il0p/BQRPy1E3k+C5wjaS1SXcVepKk5zcysm+XpvPY9Ul3CWqQO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ef82670668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QTWlh4SkGk3cQdRTCspu143vwE3qaLkCrOLjkW/j6PNg+AzpNrDx2JlOUCyu9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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ef825acf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "E1a, E1b, E2 = 1, 3, 5\n",
    "animal, day = 'Bon', 'Day3'\n",
    "evt_idx = 0 # look at paper events, 0, 13, 16, 2\n",
    "\n",
    "# Also, look at R2-sig, HMM-non-sig @ P < 0.05: 10 18 19 21  ---> all seem to be CORRECTLY discarded by HMM?\n",
    "# Also, look at R2-sig, HMM-non-sig @ P < 0.03: 10 15 18 19 21 26 34\n",
    "\n",
    "bst = data[animal][day]['remote_replay_E1_in_E2']['bst_remote_candidates'][evt_idx]\n",
    "tc = data[animal][day]['tuning_curves1D_center'][E1b]\n",
    "evt_extent = bst.support\n",
    "plot_extent = evt_extent.expand(0.05)\n",
    "st = data[animal][day]['remote_replay_E1_in_E2']['st_placecells_remote'][plot_extent]\n",
    "peak_order = tc._unit_subset(st.unit_ids).get_peak_firing_order_ids()\n",
    "\n",
    "ax = npl.rasterplot(st.reorder_units_by_ids(peak_order), vertstack=True, lw=2.5)\n",
    "npl.epochplot(plot_extent-evt_extent, hatch='', color='0.9')\n",
    "ax.set_xlim(*st.support.time)\n",
    "npl.add_scalebar(ax=ax, sizex=0.1, labelx='100 ms', hidey=False, hidex=False)\n",
    "npl.utils.clear_right()\n",
    "npl.utils.clear_top_bottom()\n",
    "plt.ylabel('E1 place cells')\n",
    "plt.xlabel('Time')\n",
    "# ymin, ymax = ax.get_ylim()\n",
    "posterior, lengths, mode_pth, mean_pth = nel.decoding.decode1D(bst=bst, ratemap=tc.smooth(sigma=4))\n",
    "# plt.plot(bst.bin_centers, mode_pth*ymax / tc.bin_centers[-1])\n",
    "\n",
    "divider = make_axes_locatable(ax)\n",
    "axBins = divider.append_axes(\"top\", size=0.3, pad=0.1)\n",
    "\n",
    "bins = np.atleast_2d(posterior.sum(axis=0))\n",
    "non_empty_idx = np.argwhere(~np.isnan(bins))[:,1]\n",
    "n_non_empty = len(non_empty_idx)\n",
    "bins[:,non_empty_idx] = np.arange(n_non_empty)\n",
    "\n",
    "NUM_COLORS = n_non_empty\n",
    "cm = plt.get_cmap('magma')\n",
    "cm = plt.get_cmap('jet')\n",
    "clist = [cm(1.*i/NUM_COLORS) for i in range(NUM_COLORS)]\n",
    "npl.set_palette(clist)\n",
    "nan_jet = ListedColormap(clist, name='nan_jet')\n",
    "\n",
    "axBins.pcolor(bst.bins, [0,1,], bins, cmap=nan_jet)\n",
    "axBins.set_xlim(ax.get_xlim())\n",
    "npl.utils.clear_left_right(axBins)\n",
    "npl.utils.clear_top_bottom(axBins)\n",
    "\n",
    "axBins.set_title('{} {} remote candidate {} in E1 center-outer ordering'.format(animal, day, evt_idx), y=1.2)\n",
    "plt.show()\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(6, 1.5))\n",
    "for post in posterior.T:\n",
    "    if not any(np.isnan(post)):\n",
    "        plt.plot(tc.bin_centers, post, lw=2);\n",
    "plt.xlabel('Decoded distance to center endpoint (cm)')\n",
    "plt.ylabel('Probability')\n",
    "npl.utils.clear_right()\n",
    "npl.utils.clear_top()\n",
    "plt.show()\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(6, 1.5))\n",
    "sns.distplot\n",
    "\n",
    "scores = data[animal][day]['remote_replay_E1_in_E2']['pvals_remote_candidates']\n",
    "tswap = data[animal][day]['remote_replay_E1_in_E2']['scores_tswap_hmm']\n",
    "\n",
    "evt_idx = 16\n",
    "sns.distplot(tswap[:,evt_idx], hist=False)\n",
    "plt.vlines(scores[evt_idx], 0,1)\n",
    "plt.title(evt_idx)\n",
    "npl.savefig('hmm-tswap-{}'.format(evt_idx))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression demo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I am still missing something. Did Mattias sample from P(X|C) AND perform a time swap shuffle? The description is still a little unclear or hard to parse, to me. Since sampling from tight posteriors doesn't do much, for computational efficiency I will do an approximate version now, where I only do time swap regressions on the modes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import copy\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy.misc import derivative\n",
    "from types import LambdaType\n",
    "from math import isnan, log\n",
    "\n",
    "\n",
    "class _BaseSampling(object):\n",
    "    # Base class for samplepy sampling package\n",
    "    \n",
    "   \n",
    "    def __check_function__(self, f):\n",
    "        # Checks if the passed function is a lambda function\n",
    "        \n",
    "        return isinstance(f, LambdaType) and f.__name__ == \"<lambda>\"\n",
    "        \n",
    "        \n",
    "    def __check_defined_over_interval__(self, f, interval):\n",
    "        # Checks if the passed lambda is defined over the specified interval\n",
    "        \n",
    "        if interval[0]< interval[1]:\n",
    "            try:\n",
    "                if not isnan(derivative(f, interval[1], dx=1e-6)) and not isnan(derivative(f, interval[0], dx=1e-6)):\n",
    "                    return True\n",
    "                else:\n",
    "                    return False\n",
    "                \n",
    "            except:\n",
    "                raise ValueError(\"The function is not defined over the entire interval.\")\n",
    "        else:\n",
    "            raise ValueError(\"Invalid interval: interval[0] >= interval[1].\")\n",
    "            \n",
    "class Rejection(_BaseSampling):\n",
    "    \"\"\"\n",
    "       Implements rejection sampling for a specified function over a specififed interval\n",
    "    \"\"\"\n",
    "\n",
    "\n",
    "    def __init__(self, f, interval=[0.0, 1.0]):\n",
    "        # Constructor accepts the lambda function and the interval over which it should be defined\n",
    "\n",
    "        if self.__check_function__(f):\n",
    "            self._f = f\n",
    "        else:\n",
    "            raise ValueError(\"Invalid function provided.\")\n",
    "#         if self.__check_defined_over_interval__(f, interval):\n",
    "#             self._interval = interval\n",
    "#         else:\n",
    "#             raise ValueError(\"The function is not defined over the entire interval.\")\n",
    "        self._interval = interval\n",
    "        self._sample = np.array([])\n",
    "        self.n_dims = len(np.atleast_1d(f((interval[1] - interval[0])/2)))\n",
    "\n",
    "    def __repr__(self):\n",
    "\n",
    "        return \"multivariate rejection Sampling object, based on samplepy\"\n",
    "\n",
    "    def __len__(self):\n",
    "\n",
    "        return len(self._sample)\n",
    "\n",
    "    def __getitem__(self, position):\n",
    "\n",
    "        return self._sample[position]\n",
    "\n",
    "    def sample(self, sample_size, seed=None):\n",
    "        \"\"\"\n",
    "         Create a sample set of sample_size samples\n",
    "         seed (optional, default = 1) to seed the random number generator\n",
    "        \"\"\"\n",
    "\n",
    "        if sample_size < 1:\n",
    "            raise ValueError(\"N is not > 1.\")\n",
    "\n",
    "        # seed the random number generator\n",
    "        if seed:\n",
    "            np.random.seed(seed)\n",
    "\n",
    "        # calculate the min&max of f(x) to scale u2\n",
    "        x = np.arange(self._interval[0], self._interval[1],\n",
    "                      (abs(self._interval[1]-self._interval[0]))/float(max(sample_size,100)))\n",
    "        fx = self._f(x)\n",
    "        max_fx = np.atleast_1d(np.nanmax(fx, axis=-1))\n",
    "        min_fx = np.atleast_1d(np.nanmin(fx, axis=-1))\n",
    "\n",
    "        self._sample = np.empty((self.n_dims, sample_size))\n",
    "        self._sample[:] = np.nan\n",
    "\n",
    "        for dd in range(self.n_dims):\n",
    "            i=0\n",
    "            if any(np.isnan([min_fx[dd], max_fx[dd]])):\n",
    "                continue\n",
    "                \n",
    "            while i < sample_size:\n",
    "                u1 = np.random.uniform(self._interval[0], self._interval[1])\n",
    "                fu1 = np.atleast_1d(self._f(u1))[dd]  # _f(u1) is of shape (n_dims, n_samples)         \n",
    "            \n",
    "                u2 = np.random.uniform(min_fx[dd], max_fx[dd])\n",
    "\n",
    "                # collect a full sample here\n",
    "                if u2 <= fu1:\n",
    "                    self._sample[dd,i] = u1\n",
    "                    i += 1\n",
    "\n",
    "        if self.n_dims == 1:\n",
    "            self._sample = self._sample.squeeze()\n",
    "            \n",
    "        return copy.copy(self._sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sample from P(X|N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Cyq9au1SmnbKAECQnTsIII4qoOtP4mpNsLoJpUNZG6HM4+Bb7PfYMyE6DnRmtWizTPllA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\n8OEOdDtCuP2muRQXN83qiYd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OYv7CdIZ8fhnP95hKeR3/BKWlbj7/vJzf/jae8PCG24Kr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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e515836ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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/X9VqizGG7e1tdHZ2KupM+MYbbxzFVEJnlArw0wBx7SM3CjSdTuP06dPS7/fv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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e514fa7cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x1e513a57ba8>"
      ]
     },
     "execution_count": 379,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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q6g4++eQqrfonEuHKlYvj+ed7sWrV3Vx/fQvefXcR9eu/xp///G+WLt3pdbyI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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e51513aef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evt_idx = 0\n",
    "evt = data[animal][day]['remote_replay_E1_in_E2']['bst_remote_candidates'][evt_idx]\n",
    "posterior, lengths, mode_pth, mean_pth = nel.decoding.decode1D(bst=evt, ratemap=tc.smooth(sigma=4)) # nb! smoothing has a big effect!\n",
    "\n",
    "pdf = nel.AnalogSignalArray(ydata=posterior.T, timestamps=tc.bin_centers)\n",
    "ax = npl.plot(pdf)\n",
    "ax.set_ylim(0,0.2)\n",
    "plt.show()\n",
    "\n",
    "f = lambda x: pdf.asarray(at=x).yvals\n",
    "rej = Rejection(f, [pdf.time[1], pospdf.time[-2]])\n",
    "\n",
    "sample = rej.sample(sample_size=200)\n",
    "plt.plot(sample, color='0.7');\n",
    "plt.show()\n",
    "\n",
    "import scipy.stats as stats\n",
    "\n",
    "mask = ~np.isnan(sample.sum(axis=1))\n",
    "xvals = evt.bin_centers[mask]\n",
    "yvals = sample[mask]\n",
    "r2_values = []\n",
    "for yval in yvals.T:\n",
    "    slope, intercept, r_value, p_value, std_err = stats.linregress(xvals, yval)\n",
    "    r2_values.append(r_value**2)\n",
    "    \n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(evt.bin_centers[mask], mode_pth[mask])\n",
    "actual_r2 = r_value**2\n",
    "    \n",
    "sns.distplot(r2_values)\n",
    "plt.vlines(actual_r2, 0,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Time swap regression analysis on posterior modes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.00000000e+00,   0.00000000e+00,   9.79000000e-02,\n",
       "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "         2.00000000e-04,   2.55050000e-01,   2.21500000e-01,\n",
       "         2.20000000e-03,   1.37500000e-02,   2.66150000e-01,\n",
       "         8.54000000e-02,   6.50500000e-01,   4.07500000e-02,\n",
       "         3.00000000e-04,   0.00000000e+00,   2.03700000e-01,\n",
       "         1.35000000e-02,   7.70000000e-03,   1.92450000e-01,\n",
       "         0.00000000e+00,   1.00000000e-03,   0.00000000e+00,\n",
       "         2.61000000e-01,   1.60550000e-01,   1.00000000e-04,\n",
       "         4.82150000e-01,   2.00000000e-04,   4.03700000e-01,\n",
       "         2.00000000e-04,   2.40000000e-03,   8.40000000e-02,\n",
       "         6.00000000e-04,   4.55500000e-02,   1.00000000e-04])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[animal][day]['remote_replay_E1_in_E2']['pvals_remote_candidates']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['HMM_E2', 'tuning_curves1D_outer', 'tuning_curves1D_center', 'run_epochs', 'remote_replay_E1_in_E2', 'tuning_curves2D_ideal', 'HMM_E1', 'tuning_curves2D', 'pos_linear_outer_ordering', 'spikes', 'PlaceCellIDs', 'cell_metadata', 'pos_ideal', 'task_metadata', 'pos', 'task_epochs', 'speed', 'pos_linear_center_ordering', 'ripple_epochs', 'VTC_E1', 'VTC_E2'])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[animal][day].keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pval: 0.0115\n"
     ]
    },
    {
     "data": {
      "image/png": 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6fCMwJ9Z194A2+QKQ1Lp8p9qkbbtU4F3g70BxrOuOdZsAhcDHwIDW99mxrruH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ef922835f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# evts 0 and 1 are good by eye, 2, 7 are not...\n",
    "\n",
    "# R2 False Positive Bon Day3 remote evt 10 is only false positive by tc outer-E1b\n",
    "evt_idx = 10\n",
    "tc = data[animal][day]['tuning_curves1D_outer'][E1b] \n",
    "evt = data[animal][day]['remote_replay_E1_in_E2']['bst_remote_candidates'][evt_idx]\n",
    "posterior, lengths, mode_pth, mean_pth = nel.decoding.decode1D(bst=evt, ratemap=tc.smooth(sigma=4)) # nb! smoothing has a big effect!\n",
    "\n",
    "mask = ~np.isnan(mode_pth)\n",
    "xvals = evt.bin_centers[mask]\n",
    "yvals = mode_pth[mask]\n",
    "\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(xvals, yvals)\n",
    "actual_r2 = r_value**2\n",
    "\n",
    "n_shuffles = 10000\n",
    "r2_values = []\n",
    "for nn in range(n_shuffles):\n",
    "    slope, intercept, r_value, p_value, std_err = stats.linregress(xvals, np.random.permutation(yvals))\n",
    "    r2_values.append(r_value**2)\n",
    "    \n",
    "sns.distplot(r2_values)\n",
    "plt.vlines(actual_r2, 0,1)\n",
    "\n",
    "pval = (100 - stats.percentileofscore(r2_values, actual_r2))/100\n",
    "print('pval:', pval)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compute time swap p-values for all events"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def score_events_r2(bst, tc, n_shuffles=100, sigma=3):\n",
    "    \"\"\"Score, and optionally smooth tuning curves when decoding\"\"\"\n",
    "    n_events = bst.n_epochs\n",
    "    pvals = np.empty(n_events)\n",
    "    pvals[:] = np.nan\n",
    "    \n",
    "    for evt_idx in range(n_events):\n",
    "        evt = bst[evt_idx]\n",
    "        _, _, mode_pth, _ = nel.decoding.decode1D(bst=evt, ratemap=tc.smooth(sigma=sigma))\n",
    "\n",
    "        mask = ~np.isnan(mode_pth)\n",
    "        xvals = evt.bin_centers[mask]\n",
    "        yvals = mode_pth[mask]\n",
    "\n",
    "        slope, intercept, r_value, p_value, std_err = stats.linregress(xvals, yvals)\n",
    "        actual_r2 = r_value**2\n",
    "\n",
    "        r2_values = []\n",
    "        for nn in range(n_shuffles):\n",
    "            slope, intercept, r_value, p_value, std_err = stats.linregress(xvals, np.random.permutation(yvals))\n",
    "            r2_values.append(r_value**2)\n",
    "\n",
    "        pvals[evt_idx] = (100 - stats.percentileofscore(r2_values, actual_r2))/100\n",
    "        \n",
    "    return pvals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**TODO:** I just pick the smallest p-value, but I should probably return where it came from (i.e., which ordering, and whether it is E1a or E1b) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bon Day3\n",
      "scoring remote replay candidates...\n",
      "scoring local replay candidates...\n"
     ]
    }
   ],
   "source": [
    "n_shuffles = 10000\n",
    "sigma_tc = 3 # cm smoothing\n",
    "\n",
    "for animal, day in [sessions[1]]:\n",
    "    print(animal, day)\n",
    "    try:\n",
    "        bst = data[animal][day]['remote_replay_E1_in_E2']['bst_remote_candidates']\n",
    "    except KeyError:\n",
    "        print('The (animal, day) pair does not have remote replay analysis results; skipping...')\n",
    "        continue\n",
    "    \n",
    "    ############ remote candidates ############\n",
    "    print('scoring remote replay candidates...')\n",
    "    bst = data[animal][day]['remote_replay_E1_in_E2']['bst_remote_candidates']\n",
    "\n",
    "    # compute pvals of remote candidates using center-ordering from E1a\n",
    "    tc = data[animal][day]['tuning_curves1D_center'][E1a]\n",
    "    pvals_E1a_co = score_events_r2(bst=bst, tc=tc, n_shuffles=n_shuffles, sigma=sigma_tc)\n",
    "    # compute pvals of remote candidates using center-ordering from E1b\n",
    "    tc = data[animal][day]['tuning_curves1D_center'][E1b]\n",
    "    pvals_E1b_co = score_events_r2(bst=bst, tc=tc, n_shuffles=n_shuffles, sigma=sigma_tc)\n",
    "    # compute pvals of remote candidates using outer-ordering from E1a\n",
    "    tc = data[animal][day]['tuning_curves1D_outer'][E1a]\n",
    "    pvals_E1a_oo = score_events_r2(bst=bst, tc=tc, n_shuffles=n_shuffles, sigma=sigma_tc)\n",
    "    # compute pvals of remote candidates using outerr-ordering from E1b\n",
    "    tc = data[animal][day]['tuning_curves1D_outer'][E1b]\n",
    "    pvals_E1b_oo = score_events_r2(bst=bst, tc=tc, n_shuffles=n_shuffles, sigma=sigma_tc)\n",
    "    \n",
    "    pvals = np.vstack((pvals_E1a_co, pvals_E1b_co, pvals_E1a_oo, pvals_E1b_oo)).min(axis=0)\n",
    "    data[animal][day]['remote_replay_E1_in_E2']['pvals_remote_candidates'] = pvals\n",
    "           \n",
    "    ############ local candidates ############\n",
    "    print('scoring local replay candidates...')\n",
    "    bst = data[animal][day]['remote_replay_E1_in_E2']['bst_local_candidates']\n",
    "\n",
    "    # compute pvals of local candidates using center-ordering from E2\n",
    "    tc = data[animal][day]['tuning_curves1D_center'][E2]\n",
    "    pvals_E2_co = score_events_r2(bst=bst, tc=tc, n_shuffles=n_shuffles, sigma=sigma_tc)\n",
    "    # compute pvals of remote candidates using outer-ordering from E2\n",
    "    tc = data[animal][day]['tuning_curves1D_outer'][E2]\n",
    "    pvals_E2_oo = score_events_r2(bst=bst, tc=tc, n_shuffles=n_shuffles, sigma=sigma_tc)\n",
    "    \n",
    "    pvals = np.vstack((pvals_E2_co, pvals_E2_oo)).min(axis=0)\n",
    "    data[animal][day]['remote_replay_E1_in_E2']['pvals_local_candidates'] = pvals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  3,  4,  5,  6,  9, 10, 14, 15, 16, 18, 19, 21, 22, 23, 26,\n",
       "       28, 30, 31, 33, 34, 35], dtype=int64)"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "animal, day = 'Bon', 'Day3'\n",
    "\n",
    "np.argwhere(data[animal][day]['remote_replay_E1_in_E2']['pvals_remote_candidates'] < 0.05).squeeze()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've scored remote replay [of E1] in E2, we can do a few checks to see if we're still in line...\n",
    "\n",
    "> Despite the distinct representations of environment 1 and environment 2, 182 of 442 (41.2%) candidate replay events showed statistically significant replay (P < 0.05) of environment 1 when rats were located in environment 2 (Z=12.67, P<1e-10, **Fig. 4a-1** and **supplementary Figs. 6** and **7** online).\n",
    "\n",
    "> As expected, there were also many replays of environment 2; 147 of 330 (44.6%) candidate events were significant (Z=14.45, P<10e-10).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "270 of 623 (43.3%) candidate replay events showed statistically significant replay (P < 0.05) of environment 1 when rats were located in environment 2.\n",
      "\n",
      "As expected, there were also many replays of environment 2; 101 of 424 (23.8%) candidate events were significant.\n"
     ]
    }
   ],
   "source": [
    "n_sig_local = 0\n",
    "n_tot_local = 0\n",
    "\n",
    "n_sig_remote = 0\n",
    "n_tot_remote = 0\n",
    "\n",
    "for animal, day in sessions:\n",
    "    try:\n",
    "        # local\n",
    "        x = data[animal][day]['remote_replay_E1_in_E2']['pvals_local_candidates']\n",
    "        n_sig_local += np.count_nonzero(x<0.05)\n",
    "        n_tot_local += len(x)\n",
    "        # remote\n",
    "        x = data[animal][day]['remote_replay_E1_in_E2']['pvals_remote_candidates']\n",
    "        n_sig_remote += np.count_nonzero(x<0.05)\n",
    "        n_tot_remote += len(x)\n",
    "    except KeyError:\n",
    "        continue\n",
    "\n",
    "print('{} of {} ({:1.1f}%) candidate replay events showed statistically significant replay (P < 0.05) of environment 1 when rats were located in environment 2.'.format(n_sig_remote, n_tot_remote, n_sig_remote/n_tot_remote*100))\n",
    "print('\\nAs expected, there were also many replays of environment 2; {} of {} ({:1.1f}%) candidate events were significant.'.format(n_sig_local, n_tot_local, n_sig_local/n_tot_local*100))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Save augmented data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "FrankLabData = nel.ResultsContainer(data=data,\n",
    "                                    sessions=FrankLabData.sessions,\n",
    "                                    cellinfo=FrankLabData.cellinfo,\n",
    "                                    taskinfo=FrankLabData.taskinfo,\n",
    "                                    tetinfo=FrankLabData.tetinfo,\n",
    "                                    description=FrankLabData.description)\n",
    "\n",
    "FrankLabData.save_pkl(fileroot + outfile)"
   ]
  }
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