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2 changes: 1 addition & 1 deletion .nojekyll
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3 changes: 2 additions & 1 deletion schedule/slides/18-the-bootstrap.html
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<h2>18 The bootstrap</h2>
<p><span class="secondary">Stat 406</span></p>
<p><span class="secondary">Geoff Pleiss, Trevor Campbell</span></p>
<p>Last modified – 28 October 2024</p>
<p>Last modified – 29 October 2024</p>
<p><span class="math display">\[
\DeclareMathOperator*{\argmin}{argmin}
\DeclareMathOperator*{\argmax}{argmax}
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<li>Produce the original estimate <span class="math inline">\(\hat\theta=\widehat{\Pr}(Y_0=1 \given X_0)\)</span></li>
<li>Resample your training data <span class="math inline">\(B\)</span> times with replacement</li>
<li>Refit LDA for each one to produce <span class="math inline">\(\widehat{\Pr}\nolimits_b(Y_0 =1 \given X_0)\)</span>.</li>
<li>Variance: empirical variance of <span class="math inline">\(\widehat{\Pr}\nolimits_b(Y_0 =1 \given X_0)\)</span>.</li>
<li>CI: <span class="math inline">\(\left[2\widehat{\Pr}(Y_0 =1 \given X_0) - \widehat{F}_{\text{boot}}(1-\alpha/2),\ 2\widehat{\Pr}(Y_0 =1 \given X_0) - \widehat{F}_{\text{boot}}(\alpha/2)\right]\)</span>
<ul>
<li><span class="math inline">\(\widehat{F}_{\text{boot}}\)</span> is the empirical CDF of the samples <span class="math inline">\(\widehat{\Pr}\nolimits_b(Y_0 =1 \given X_0)\)</span></li>
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4 changes: 2 additions & 2 deletions search.json
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"text": "18 The bootstrap\nStat 406\nGeoff Pleiss, Trevor Campbell\nLast modified – 29 October 2024\n\\[\n\\DeclareMathOperator*{\\argmin}{argmin}\n\\DeclareMathOperator*{\\argmax}{argmax}\n\\DeclareMathOperator*{\\minimize}{minimize}\n\\DeclareMathOperator*{\\maximize}{maximize}\n\\DeclareMathOperator*{\\find}{find}\n\\DeclareMathOperator{\\st}{subject\\,\\,to}\n\\newcommand{\\E}{E}\n\\newcommand{\\Expect}[1]{\\E\\left[ #1 \\right]}\n\\newcommand{\\Var}[1]{\\mathrm{Var}\\left[ #1 \\right]}\n\\newcommand{\\Cov}[2]{\\mathrm{Cov}\\left[#1,\\ #2\\right]}\n\\newcommand{\\given}{\\ \\vert\\ }\n\\newcommand{\\X}{\\mathbf{X}}\n\\newcommand{\\x}{\\mathbf{x}}\n\\newcommand{\\y}{\\mathbf{y}}\n\\newcommand{\\P}{\\mathcal{P}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\norm}[1]{\\left\\lVert #1 \\right\\rVert}\n\\newcommand{\\snorm}[1]{\\lVert #1 \\rVert}\n\\newcommand{\\tr}[1]{\\mbox{tr}(#1)}\n\\newcommand{\\brt}{\\widehat{\\beta}^R_{s}}\n\\newcommand{\\brl}{\\widehat{\\beta}^R_{\\lambda}}\n\\newcommand{\\bls}{\\widehat{\\beta}_{ols}}\n\\newcommand{\\blt}{\\widehat{\\beta}^L_{s}}\n\\newcommand{\\bll}{\\widehat{\\beta}^L_{\\lambda}}\n\\newcommand{\\U}{\\mathbf{U}}\n\\newcommand{\\D}{\\mathbf{D}}\n\\newcommand{\\V}{\\mathbf{V}}\n\\]"
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"section": "The bootstrap is very flexible",
"text": "The bootstrap is very flexible\ne.g., for LDA:\n\nProduce the original estimate \\(\\hat\\theta=\\widehat{\\Pr}(Y_0=1 \\given X_0)\\)\nResample your training data \\(B\\) times with replacement\nRefit LDA for each one to produce \\(\\widehat{\\Pr}\\nolimits_b(Y_0 =1 \\given X_0)\\).\nCI: \\(\\left[2\\widehat{\\Pr}(Y_0 =1 \\given X_0) - \\widehat{F}_{\\text{boot}}(1-\\alpha/2),\\ 2\\widehat{\\Pr}(Y_0 =1 \\given X_0) - \\widehat{F}_{\\text{boot}}(\\alpha/2)\\right]\\)\n\n\\(\\widehat{F}_{\\text{boot}}\\) is the empirical CDF of the samples \\(\\widehat{\\Pr}\\nolimits_b(Y_0 =1 \\given X_0)\\)"
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