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Jonathan Berrisch
2025-06-22 16:45:20 +02:00
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@@ -26162,28 +26162,22 @@ Berrisch, J. <span class="citation" data-cites="berrisch2025rcpptimer">(<a href=
<section id="the-framework-of-prediction-under-expert-advice" class="slide level2"> <section id="the-framework-of-prediction-under-expert-advice" class="slide level2">
<h2>The Framework of Prediction under Expert Advice</h2> <h2>The Framework of Prediction under Expert Advice</h2>
<h3 id="section"> </h3> <h3 id="section"> </h3>
<div class="columns">
<div class="column" style="width:48%;">
<p>Each day, <span class="math inline">\(t = 1, 2, ... T\)</span></p> <p>Each day, <span class="math inline">\(t = 1, 2, ... T\)</span></p>
<ul> <ul>
<li>The <strong>forecaster</strong> receives predictions <span class="math inline">\(\widehat{X}_{t,k}\)</span> from <span class="math inline">\(K\)</span> <strong>experts</strong></li> <li>The <strong>forecaster</strong> receives predictions <span class="math inline">\(\widehat{X}_{t,k}\)</span> from <span class="math inline">\(K\)</span> <strong>experts</strong></li>
<li>The <strong>forecaster</strong> assigns weights <span class="math inline">\(w_{t,k}\)</span> to each <strong>expert</strong></li> <li>The <strong>forecaster</strong> assigns weights <span class="math inline">\(w_{t,k}\)</span> to each <strong>expert</strong></li>
<li>The <strong>forecaster</strong> calculates her prediction: <span class="math display">\[\begin{equation} <li>The <strong>forecaster</strong> calculates the prediction:</li>
</ul>
<p><span class="math display">\[\begin{equation}
\widetilde{X}_{t} = \sum_{k=1}^K w_{t,k} \widehat{X}_{t,k}. \widetilde{X}_{t} = \sum_{k=1}^K w_{t,k} \widehat{X}_{t,k}.
\label{eq_forecast_def} \label{eq_forecast_def}
\end{equation}\]</span></li> \end{equation}\]</span></p>
<ul>
<li>The realization for <span class="math inline">\(t\)</span> is observed</li> <li>The realization for <span class="math inline">\(t\)</span> is observed</li>
</ul> </ul>
</div><div class="column" style="width:4%;"> <p><i class="fa fa-fw fa-arrow-right" style="color:var(--col_grey_9);"></i> The experts can be institutions, persons, or models</p>
<p><i class="fa fa-fw fa-arrow-right" style="color:var(--col_grey_9);"></i> The forecasts can be point-forecasts (i.e., mean or median) or full predictive distributions</p>
</div><div class="column" style="width:48%;"> <p><i class="fa fa-fw fa-arrow-right" style="color:var(--col_grey_9);"></i> <span class="citation" data-cites="cesa2006prediction">Cesa-Bianchi &amp; Lugosi (<a href="#/references" role="doc-biblioref" onclick>2006</a>)</span></p>
<ul>
<li>The experts can be institutions, persons, or models</li>
<li>The forecasts can be point-forecasts (i.e., mean or median) or full predictive distributions</li>
<li>We do not need a distributional assumption concerning the underlying data</li>
<li><span class="citation" data-cites="cesa2006prediction">Cesa-Bianchi &amp; Lugosi (<a href="#/references" role="doc-biblioref" onclick>2006</a>)</span></li>
</ul>
</div></div>
</section> </section>
<section id="the-regret" class="slide level2"> <section id="the-regret" class="slide level2">
<h2>The Regret</h2> <h2>The Regret</h2>
@@ -27226,7 +27220,7 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \
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<div class="sourceCode cell-code hidden" id="cb5" data-startfrom="2691" data-source-offset="0"><pre class="sourceCode numberSource js number-lines code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 2690;"><span id="cb5-2691"><a href></a>bsplineData <span class="op">=</span> <span class="fu">FileAttachment</span>(<span class="st">&quot;assets/mcrps_learning/basis_functions.csv&quot;</span>)<span class="op">.</span><span class="fu">csv</span>({ <span class="dt">typed</span><span class="op">:</span> <span class="kw">true</span> })</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> <div class="sourceCode cell-code hidden" id="cb5" data-startfrom="2676" data-source-offset="0"><pre class="sourceCode numberSource js number-lines code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 2675;"><span id="cb5-2676"><a href></a>bsplineData <span class="op">=</span> <span class="fu">FileAttachment</span>(<span class="st">&quot;assets/mcrps_learning/basis_functions.csv&quot;</span>)<span class="op">.</span><span class="fu">csv</span>({ <span class="dt">typed</span><span class="op">:</span> <span class="kw">true</span> })</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display"> <div class="cell-output cell-output-display">
<div id="ojs-cell-4" data-nodetype="declaration"> <div id="ojs-cell-4" data-nodetype="declaration">
@@ -27234,194 +27228,194 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \
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<div class="sourceCode cell-code hidden" id="cb6" data-startfrom="2695" data-source-offset="0"><pre class="sourceCode numberSource js number-lines code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 2694;"><span id="cb6-2695"><a href></a><span class="co">// Defined above</span></span> <div class="sourceCode cell-code hidden" id="cb6" data-startfrom="2680" data-source-offset="0"><pre class="sourceCode numberSource js number-lines code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 2679;"><span id="cb6-2680"><a href></a><span class="co">// Defined above</span></span>
<span id="cb6-2696"><a href></a><span class="co">// function updateChartInner(g, x, y, linesGroup, color, line, data) {</span></span> <span id="cb6-2681"><a href></a><span class="co">// function updateChartInner(g, x, y, linesGroup, color, line, data) {</span></span>
<span id="cb6-2697"><a href></a><span class="co">// // Update axes with transitions</span></span> <span id="cb6-2682"><a href></a><span class="co">// // Update axes with transitions</span></span>
<span id="cb6-2698"><a href></a><span class="co">// x.domain([0, d3.max(data, d =&gt; d.x)]);</span></span> <span id="cb6-2683"><a href></a><span class="co">// x.domain([0, d3.max(data, d =&gt; d.x)]);</span></span>
<span id="cb6-2699"><a href></a><span class="co">// g.select(&quot;.x-axis&quot;).transition().duration(1500).call(d3.axisBottom(x).ticks(10));</span></span> <span id="cb6-2684"><a href></a><span class="co">// g.select(&quot;.x-axis&quot;).transition().duration(1500).call(d3.axisBottom(x).ticks(10));</span></span>
<span id="cb6-2700"><a href></a><span class="co">// y.domain([0, d3.max(data, d =&gt; d.y)]);</span></span> <span id="cb6-2685"><a href></a><span class="co">// y.domain([0, d3.max(data, d =&gt; d.y)]);</span></span>
<span id="cb6-2701"><a href></a><span class="co">// g.select(&quot;.y-axis&quot;).transition().duration(1500).call(d3.axisLeft(y).ticks(5));</span></span> <span id="cb6-2686"><a href></a><span class="co">// g.select(&quot;.y-axis&quot;).transition().duration(1500).call(d3.axisLeft(y).ticks(5));</span></span>
<span id="cb6-2702"><a href></a></span> <span id="cb6-2687"><a href></a></span>
<span id="cb6-2703"><a href></a><span class="co">// // Group data by basis function</span></span> <span id="cb6-2688"><a href></a><span class="co">// // Group data by basis function</span></span>
<span id="cb6-2704"><a href></a><span class="co">// const dataByFunction = Array.from(d3.group(data, d =&gt; d.b));</span></span> <span id="cb6-2689"><a href></a><span class="co">// const dataByFunction = Array.from(d3.group(data, d =&gt; d.b));</span></span>
<span id="cb6-2705"><a href></a><span class="co">// const keyFn = d =&gt; d[0];</span></span> <span id="cb6-2690"><a href></a><span class="co">// const keyFn = d =&gt; d[0];</span></span>
<span id="cb6-2691"><a href></a></span>
<span id="cb6-2692"><a href></a><span class="co">// // Update basis function lines</span></span>
<span id="cb6-2693"><a href></a><span class="co">// const u = linesGroup.selectAll(&quot;path&quot;).data(dataByFunction, keyFn);</span></span>
<span id="cb6-2694"><a href></a><span class="co">// u.join(</span></span>
<span id="cb6-2695"><a href></a><span class="co">// enter =&gt; enter.append(&quot;path&quot;).attr(&quot;fill&quot;,&quot;none&quot;).attr(&quot;stroke-width&quot;,3)</span></span>
<span id="cb6-2696"><a href></a><span class="co">// .attr(&quot;stroke&quot;, (_, i) =&gt; color(i)).attr(&quot;d&quot;, d =&gt; line(d[1].map(pt =&gt; ({x: pt.x, y: 0}))))</span></span>
<span id="cb6-2697"><a href></a><span class="co">// .style(&quot;opacity&quot;,0),</span></span>
<span id="cb6-2698"><a href></a><span class="co">// update =&gt; update,</span></span>
<span id="cb6-2699"><a href></a><span class="co">// exit =&gt; exit.transition().duration(1000).style(&quot;opacity&quot;,0).remove()</span></span>
<span id="cb6-2700"><a href></a><span class="co">// )</span></span>
<span id="cb6-2701"><a href></a><span class="co">// .transition().duration(1000)</span></span>
<span id="cb6-2702"><a href></a><span class="co">// .attr(&quot;d&quot;, d =&gt; line(d[1]))</span></span>
<span id="cb6-2703"><a href></a><span class="co">// .attr(&quot;stroke&quot;, (_, i) =&gt; color(i))</span></span>
<span id="cb6-2704"><a href></a><span class="co">// .style(&quot;opacity&quot;,1);</span></span>
<span id="cb6-2705"><a href></a><span class="co">// }</span></span>
<span id="cb6-2706"><a href></a></span> <span id="cb6-2706"><a href></a></span>
<span id="cb6-2707"><a href></a><span class="co">// // Update basis function lines</span></span> <span id="cb6-2707"><a href></a>chart0 <span class="op">=</span> {</span>
<span id="cb6-2708"><a href></a><span class="co">// const u = linesGroup.selectAll(&quot;path&quot;).data(dataByFunction, keyFn);</span></span> <span id="cb6-2708"><a href></a> <span class="co">// State variables for selected parameters</span></span>
<span id="cb6-2709"><a href></a><span class="co">// u.join(</span></span> <span id="cb6-2709"><a href></a> <span class="kw">let</span> selectedMu <span class="op">=</span> <span class="fl">0.5</span><span class="op">;</span></span>
<span id="cb6-2710"><a href></a><span class="co">// enter =&gt; enter.append(&quot;path&quot;).attr(&quot;fill&quot;,&quot;none&quot;).attr(&quot;stroke-width&quot;,3)</span></span> <span id="cb6-2710"><a href></a> <span class="kw">let</span> selectedSig <span class="op">=</span> <span class="dv">1</span><span class="op">;</span></span>
<span id="cb6-2711"><a href></a><span class="co">// .attr(&quot;stroke&quot;, (_, i) =&gt; color(i)).attr(&quot;d&quot;, d =&gt; line(d[1].map(pt =&gt; ({x: pt.x, y: 0}))))</span></span> <span id="cb6-2711"><a href></a> <span class="kw">let</span> selectedNonc <span class="op">=</span> <span class="dv">0</span><span class="op">;</span></span>
<span id="cb6-2712"><a href></a><span class="co">// .style(&quot;opacity&quot;,0),</span></span> <span id="cb6-2712"><a href></a> <span class="kw">let</span> selectedTailw <span class="op">=</span> <span class="dv">1</span><span class="op">;</span></span>
<span id="cb6-2713"><a href></a><span class="co">// update =&gt; update,</span></span> <span id="cb6-2713"><a href></a> <span class="kw">const</span> filteredData <span class="op">=</span> () <span class="kw">=&gt;</span> bsplineData<span class="op">.</span><span class="fu">filter</span>(d <span class="kw">=&gt;</span></span>
<span id="cb6-2714"><a href></a><span class="co">// exit =&gt; exit.transition().duration(1000).style(&quot;opacity&quot;,0).remove()</span></span> <span id="cb6-2714"><a href></a> <span class="bu">Math</span><span class="op">.</span><span class="fu">abs</span>(selectedMu <span class="op">-</span> d<span class="op">.</span><span class="at">mu</span>) <span class="op">&lt;</span> <span class="fl">0.001</span> <span class="op">&amp;&amp;</span></span>
<span id="cb6-2715"><a href></a><span class="co">// )</span></span> <span id="cb6-2715"><a href></a> d<span class="op">.</span><span class="at">sig</span> <span class="op">===</span> selectedSig <span class="op">&amp;&amp;</span></span>
<span id="cb6-2716"><a href></a><span class="co">// .transition().duration(1000)</span></span> <span id="cb6-2716"><a href></a> d<span class="op">.</span><span class="at">nonc</span> <span class="op">===</span> selectedNonc <span class="op">&amp;&amp;</span></span>
<span id="cb6-2717"><a href></a><span class="co">// .attr(&quot;d&quot;, d =&gt; line(d[1]))</span></span> <span id="cb6-2717"><a href></a> d<span class="op">.</span><span class="at">tailw</span> <span class="op">===</span> selectedTailw</span>
<span id="cb6-2718"><a href></a><span class="co">// .attr(&quot;stroke&quot;, (_, i) =&gt; color(i))</span></span> <span id="cb6-2718"><a href></a> )<span class="op">;</span></span>
<span id="cb6-2719"><a href></a><span class="co">// .style(&quot;opacity&quot;,1);</span></span> <span id="cb6-2719"><a href></a> <span class="kw">const</span> container <span class="op">=</span> d3<span class="op">.</span><span class="fu">create</span>(<span class="st">&quot;div&quot;</span>)</span>
<span id="cb6-2720"><a href></a><span class="co">// }</span></span> <span id="cb6-2720"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;max-width&quot;</span><span class="op">,</span> <span class="st">&quot;none&quot;</span>)</span>
<span id="cb6-2721"><a href></a></span> <span id="cb6-2721"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;width&quot;</span><span class="op">,</span> <span class="st">&quot;100%&quot;</span>)<span class="op">;;</span></span>
<span id="cb6-2722"><a href></a>chart0 <span class="op">=</span> {</span> <span id="cb6-2722"><a href></a> <span class="kw">const</span> controlsContainer <span class="op">=</span> container<span class="op">.</span><span class="fu">append</span>(<span class="st">&quot;div&quot;</span>)</span>
<span id="cb6-2723"><a href></a> <span class="co">// State variables for selected parameters</span></span> <span id="cb6-2723"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;display&quot;</span><span class="op">,</span> <span class="st">&quot;flex&quot;</span>)</span>
<span id="cb6-2724"><a href></a> <span class="kw">let</span> selectedMu <span class="op">=</span> <span class="fl">0.5</span><span class="op">;</span></span> <span id="cb6-2724"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;gap&quot;</span><span class="op">,</span> <span class="st">&quot;20px&quot;</span>)<span class="op">;</span></span>
<span id="cb6-2725"><a href></a> <span class="kw">let</span> selectedSig <span class="op">=</span> <span class="dv">1</span><span class="op">;</span></span> <span id="cb6-2725"><a href></a> <span class="co">// slider controls</span></span>
<span id="cb6-2726"><a href></a> <span class="kw">let</span> selectedNonc <span class="op">=</span> <span class="dv">0</span><span class="op">;</span></span> <span id="cb6-2726"><a href></a> <span class="kw">const</span> sliders <span class="op">=</span> [</span>
<span id="cb6-2727"><a href></a> <span class="kw">let</span> selectedTailw <span class="op">=</span> <span class="dv">1</span><span class="op">;</span></span> <span id="cb6-2727"><a href></a> { <span class="dt">label</span><span class="op">:</span> <span class="st">&#39;Mu&#39;</span><span class="op">,</span> <span class="kw">get</span><span class="op">:</span> () <span class="kw">=&gt;</span> selectedMu<span class="op">,</span> <span class="kw">set</span><span class="op">:</span> v <span class="kw">=&gt;</span> selectedMu <span class="op">=</span> v<span class="op">,</span> <span class="dt">min</span><span class="op">:</span> <span class="fl">0.1</span><span class="op">,</span> <span class="dt">max</span><span class="op">:</span> <span class="fl">0.9</span><span class="op">,</span> <span class="dt">step</span><span class="op">:</span> <span class="fl">0.2</span> }<span class="op">,</span></span>
<span id="cb6-2728"><a href></a> <span class="kw">const</span> filteredData <span class="op">=</span> () <span class="kw">=&gt;</span> bsplineData<span class="op">.</span><span class="fu">filter</span>(d <span class="kw">=&gt;</span></span> <span id="cb6-2728"><a href></a> { <span class="dt">label</span><span class="op">:</span> <span class="st">&#39;Sigma&#39;</span><span class="op">,</span> <span class="kw">get</span><span class="op">:</span> () <span class="kw">=&gt;</span> <span class="bu">Math</span><span class="op">.</span><span class="fu">log2</span>(selectedSig)<span class="op">,</span> <span class="kw">set</span><span class="op">:</span> v <span class="kw">=&gt;</span> selectedSig <span class="op">=</span> <span class="dv">2</span> <span class="op">**</span> v<span class="op">,</span> <span class="dt">min</span><span class="op">:</span> <span class="op">-</span><span class="dv">2</span><span class="op">,</span> <span class="dt">max</span><span class="op">:</span> <span class="dv">2</span><span class="op">,</span> <span class="dt">step</span><span class="op">:</span> <span class="dv">1</span> }<span class="op">,</span></span>
<span id="cb6-2729"><a href></a> <span class="bu">Math</span><span class="op">.</span><span class="fu">abs</span>(selectedMu <span class="op">-</span> d<span class="op">.</span><span class="at">mu</span>) <span class="op">&lt;</span> <span class="fl">0.001</span> <span class="op">&amp;&amp;</span></span> <span id="cb6-2729"><a href></a> { <span class="dt">label</span><span class="op">:</span> <span class="st">&#39;Noncentrality&#39;</span><span class="op">,</span> <span class="kw">get</span><span class="op">:</span> () <span class="kw">=&gt;</span> selectedNonc<span class="op">,</span> <span class="kw">set</span><span class="op">:</span> v <span class="kw">=&gt;</span> selectedNonc <span class="op">=</span> v<span class="op">,</span> <span class="dt">min</span><span class="op">:</span> <span class="op">-</span><span class="dv">4</span><span class="op">,</span> <span class="dt">max</span><span class="op">:</span> <span class="dv">4</span><span class="op">,</span> <span class="dt">step</span><span class="op">:</span> <span class="dv">2</span> }<span class="op">,</span></span>
<span id="cb6-2730"><a href></a> d<span class="op">.</span><span class="at">sig</span> <span class="op">===</span> selectedSig <span class="op">&amp;&amp;</span></span> <span id="cb6-2730"><a href></a> { <span class="dt">label</span><span class="op">:</span> <span class="st">&#39;Tailweight&#39;</span><span class="op">,</span> <span class="kw">get</span><span class="op">:</span> () <span class="kw">=&gt;</span> <span class="bu">Math</span><span class="op">.</span><span class="fu">log2</span>(selectedTailw)<span class="op">,</span> <span class="kw">set</span><span class="op">:</span> v <span class="kw">=&gt;</span> selectedTailw <span class="op">=</span> <span class="dv">2</span> <span class="op">**</span> v<span class="op">,</span> <span class="dt">min</span><span class="op">:</span> <span class="op">-</span><span class="dv">2</span><span class="op">,</span> <span class="dt">max</span><span class="op">:</span> <span class="dv">2</span><span class="op">,</span> <span class="dt">step</span><span class="op">:</span> <span class="dv">1</span> }</span>
<span id="cb6-2731"><a href></a> d<span class="op">.</span><span class="at">nonc</span> <span class="op">===</span> selectedNonc <span class="op">&amp;&amp;</span></span> <span id="cb6-2731"><a href></a> ]<span class="op">;</span></span>
<span id="cb6-2732"><a href></a> d<span class="op">.</span><span class="at">tailw</span> <span class="op">===</span> selectedTailw</span> <span id="cb6-2732"><a href></a> <span class="co">// Build slider controls with D3 data join</span></span>
<span id="cb6-2733"><a href></a> )<span class="op">;</span></span> <span id="cb6-2733"><a href></a> <span class="kw">const</span> sliderCont <span class="op">=</span> controlsContainer<span class="op">.</span><span class="fu">selectAll</span>(<span class="st">&#39;div&#39;</span>)<span class="op">.</span><span class="fu">data</span>(sliders)<span class="op">.</span><span class="fu">join</span>(<span class="st">&#39;div&#39;</span>)</span>
<span id="cb6-2734"><a href></a> <span class="kw">const</span> container <span class="op">=</span> d3<span class="op">.</span><span class="fu">create</span>(<span class="st">&quot;div&quot;</span>)</span> <span id="cb6-2734"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;display&#39;</span><span class="op">,</span><span class="st">&#39;flex&#39;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;align-items&#39;</span><span class="op">,</span><span class="st">&#39;center&#39;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;gap&#39;</span><span class="op">,</span><span class="st">&#39;10px&#39;</span>)</span>
<span id="cb6-2735"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;max-width&quot;</span><span class="op">,</span> <span class="st">&quot;none&quot;</span>)</span> <span id="cb6-2735"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;flex&#39;</span><span class="op">,</span><span class="st">&#39;1&#39;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;min-width&#39;</span><span class="op">,</span><span class="st">&#39;0px&#39;</span>)<span class="op">;</span></span>
<span id="cb6-2736"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;width&quot;</span><span class="op">,</span> <span class="st">&quot;100%&quot;</span>)<span class="op">;;</span></span> <span id="cb6-2736"><a href></a> sliderCont<span class="op">.</span><span class="fu">append</span>(<span class="st">&#39;label&#39;</span>)<span class="op">.</span><span class="fu">text</span>(d <span class="kw">=&gt;</span> d<span class="op">.</span><span class="at">label</span> <span class="op">+</span> <span class="st">&#39;:&#39;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;font-size&#39;</span><span class="op">,</span><span class="st">&#39;20px&#39;</span>)<span class="op">;</span></span>
<span id="cb6-2737"><a href></a> <span class="kw">const</span> controlsContainer <span class="op">=</span> container<span class="op">.</span><span class="fu">append</span>(<span class="st">&quot;div&quot;</span>)</span> <span id="cb6-2737"><a href></a> sliderCont<span class="op">.</span><span class="fu">append</span>(<span class="st">&#39;input&#39;</span>)</span>
<span id="cb6-2738"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;display&quot;</span><span class="op">,</span> <span class="st">&quot;flex&quot;</span>)</span> <span id="cb6-2738"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&#39;type&#39;</span><span class="op">,</span><span class="st">&#39;range&#39;</span>)<span class="op">.</span><span class="fu">attr</span>(<span class="st">&#39;min&#39;</span><span class="op">,</span> d <span class="kw">=&gt;</span> d<span class="op">.</span><span class="at">min</span>)<span class="op">.</span><span class="fu">attr</span>(<span class="st">&#39;max&#39;</span><span class="op">,</span> d <span class="kw">=&gt;</span> d<span class="op">.</span><span class="at">max</span>)<span class="op">.</span><span class="fu">attr</span>(<span class="st">&#39;step&#39;</span><span class="op">,</span> d <span class="kw">=&gt;</span> d<span class="op">.</span><span class="at">step</span>)</span>
<span id="cb6-2739"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;gap&quot;</span><span class="op">,</span> <span class="st">&quot;20px&quot;</span>)<span class="op">;</span></span> <span id="cb6-2739"><a href></a> <span class="op">.</span><span class="fu">property</span>(<span class="st">&#39;value&#39;</span><span class="op">,</span> d <span class="kw">=&gt;</span> d<span class="op">.</span><span class="fu">get</span>())</span>
<span id="cb6-2740"><a href></a> <span class="co">// slider controls</span></span> <span id="cb6-2740"><a href></a> <span class="op">.</span><span class="fu">on</span>(<span class="st">&#39;input&#39;</span><span class="op">,</span> <span class="kw">function</span>(<span class="bu">event</span><span class="op">,</span> d) {</span>
<span id="cb6-2741"><a href></a> <span class="kw">const</span> sliders <span class="op">=</span> [</span> <span id="cb6-2741"><a href></a> <span class="kw">const</span> val <span class="op">=</span> <span class="op">+</span><span class="kw">this</span><span class="op">.</span><span class="at">value</span><span class="op">;</span> d<span class="op">.</span><span class="fu">set</span>(val)<span class="op">;</span></span>
<span id="cb6-2742"><a href></a> { <span class="dt">label</span><span class="op">:</span> <span class="st">&#39;Mu&#39;</span><span class="op">,</span> <span class="kw">get</span><span class="op">:</span> () <span class="kw">=&gt;</span> selectedMu<span class="op">,</span> <span class="kw">set</span><span class="op">:</span> v <span class="kw">=&gt;</span> selectedMu <span class="op">=</span> v<span class="op">,</span> <span class="dt">min</span><span class="op">:</span> <span class="fl">0.1</span><span class="op">,</span> <span class="dt">max</span><span class="op">:</span> <span class="fl">0.9</span><span class="op">,</span> <span class="dt">step</span><span class="op">:</span> <span class="fl">0.2</span> }<span class="op">,</span></span> <span id="cb6-2742"><a href></a> d3<span class="op">.</span><span class="fu">select</span>(<span class="kw">this</span><span class="op">.</span><span class="at">parentNode</span>)<span class="op">.</span><span class="fu">select</span>(<span class="st">&#39;span&#39;</span>)<span class="op">.</span><span class="fu">text</span>(d<span class="op">.</span><span class="at">label</span><span class="op">.</span><span class="fu">match</span>(<span class="ss">/Sigma</span><span class="sc">|</span><span class="ss">Tailweight/</span>) <span class="op">?</span> <span class="dv">2</span><span class="op">**</span>val <span class="op">:</span> val)<span class="op">;</span></span>
<span id="cb6-2743"><a href></a> { <span class="dt">label</span><span class="op">:</span> <span class="st">&#39;Sigma&#39;</span><span class="op">,</span> <span class="kw">get</span><span class="op">:</span> () <span class="kw">=&gt;</span> <span class="bu">Math</span><span class="op">.</span><span class="fu">log2</span>(selectedSig)<span class="op">,</span> <span class="kw">set</span><span class="op">:</span> v <span class="kw">=&gt;</span> selectedSig <span class="op">=</span> <span class="dv">2</span> <span class="op">**</span> v<span class="op">,</span> <span class="dt">min</span><span class="op">:</span> <span class="op">-</span><span class="dv">2</span><span class="op">,</span> <span class="dt">max</span><span class="op">:</span> <span class="dv">2</span><span class="op">,</span> <span class="dt">step</span><span class="op">:</span> <span class="dv">1</span> }<span class="op">,</span></span> <span id="cb6-2743"><a href></a> <span class="fu">updateChart</span>(<span class="fu">filteredData</span>())<span class="op">;</span></span>
<span id="cb6-2744"><a href></a> { <span class="dt">label</span><span class="op">:</span> <span class="st">&#39;Noncentrality&#39;</span><span class="op">,</span> <span class="kw">get</span><span class="op">:</span> () <span class="kw">=&gt;</span> selectedNonc<span class="op">,</span> <span class="kw">set</span><span class="op">:</span> v <span class="kw">=&gt;</span> selectedNonc <span class="op">=</span> v<span class="op">,</span> <span class="dt">min</span><span class="op">:</span> <span class="op">-</span><span class="dv">4</span><span class="op">,</span> <span class="dt">max</span><span class="op">:</span> <span class="dv">4</span><span class="op">,</span> <span class="dt">step</span><span class="op">:</span> <span class="dv">2</span> }<span class="op">,</span></span> <span id="cb6-2744"><a href></a> })</span>
<span id="cb6-2745"><a href></a> { <span class="dt">label</span><span class="op">:</span> <span class="st">&#39;Tailweight&#39;</span><span class="op">,</span> <span class="kw">get</span><span class="op">:</span> () <span class="kw">=&gt;</span> <span class="bu">Math</span><span class="op">.</span><span class="fu">log2</span>(selectedTailw)<span class="op">,</span> <span class="kw">set</span><span class="op">:</span> v <span class="kw">=&gt;</span> selectedTailw <span class="op">=</span> <span class="dv">2</span> <span class="op">**</span> v<span class="op">,</span> <span class="dt">min</span><span class="op">:</span> <span class="op">-</span><span class="dv">2</span><span class="op">,</span> <span class="dt">max</span><span class="op">:</span> <span class="dv">2</span><span class="op">,</span> <span class="dt">step</span><span class="op">:</span> <span class="dv">1</span> }</span> <span id="cb6-2745"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;width&#39;</span><span class="op">,</span> <span class="st">&#39;100%&#39;</span>)<span class="op">;</span></span>
<span id="cb6-2746"><a href></a> ]<span class="op">;</span></span> <span id="cb6-2746"><a href></a> sliderCont<span class="op">.</span><span class="fu">append</span>(<span class="st">&#39;span&#39;</span>)<span class="op">.</span><span class="fu">text</span>(d <span class="kw">=&gt;</span> (d<span class="op">.</span><span class="at">label</span><span class="op">.</span><span class="fu">match</span>(<span class="ss">/Sigma</span><span class="sc">|</span><span class="ss">Tailweight/</span>) <span class="op">?</span> d<span class="op">.</span><span class="fu">get</span>() <span class="op">:</span> d<span class="op">.</span><span class="fu">get</span>()))</span>
<span id="cb6-2747"><a href></a> <span class="co">// Build slider controls with D3 data join</span></span> <span id="cb6-2747"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;font-size&#39;</span><span class="op">,</span><span class="st">&#39;20px&#39;</span>)<span class="op">;</span></span>
<span id="cb6-2748"><a href></a> <span class="kw">const</span> sliderCont <span class="op">=</span> controlsContainer<span class="op">.</span><span class="fu">selectAll</span>(<span class="st">&#39;div&#39;</span>)<span class="op">.</span><span class="fu">data</span>(sliders)<span class="op">.</span><span class="fu">join</span>(<span class="st">&#39;div&#39;</span>)</span> <span id="cb6-2748"><a href></a> </span>
<span id="cb6-2749"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;display&#39;</span><span class="op">,</span><span class="st">&#39;flex&#39;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;align-items&#39;</span><span class="op">,</span><span class="st">&#39;center&#39;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;gap&#39;</span><span class="op">,</span><span class="st">&#39;10px&#39;</span>)</span> <span id="cb6-2749"><a href></a> <span class="co">// Add Reset button to clear all sliders to their defaults</span></span>
<span id="cb6-2750"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;flex&#39;</span><span class="op">,</span><span class="st">&#39;1&#39;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;min-width&#39;</span><span class="op">,</span><span class="st">&#39;0px&#39;</span>)<span class="op">;</span></span> <span id="cb6-2750"><a href></a> controlsContainer<span class="op">.</span><span class="fu">append</span>(<span class="st">&#39;button&#39;</span>)</span>
<span id="cb6-2751"><a href></a> sliderCont<span class="op">.</span><span class="fu">append</span>(<span class="st">&#39;label&#39;</span>)<span class="op">.</span><span class="fu">text</span>(d <span class="kw">=&gt;</span> d<span class="op">.</span><span class="at">label</span> <span class="op">+</span> <span class="st">&#39;:&#39;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;font-size&#39;</span><span class="op">,</span><span class="st">&#39;20px&#39;</span>)<span class="op">;</span></span> <span id="cb6-2751"><a href></a> <span class="op">.</span><span class="fu">text</span>(<span class="st">&#39;Reset&#39;</span>)</span>
<span id="cb6-2752"><a href></a> sliderCont<span class="op">.</span><span class="fu">append</span>(<span class="st">&#39;input&#39;</span>)</span> <span id="cb6-2752"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;font-size&#39;</span><span class="op">,</span> <span class="st">&#39;20px&#39;</span>)</span>
<span id="cb6-2753"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&#39;type&#39;</span><span class="op">,</span><span class="st">&#39;range&#39;</span>)<span class="op">.</span><span class="fu">attr</span>(<span class="st">&#39;min&#39;</span><span class="op">,</span> d <span class="kw">=&gt;</span> d<span class="op">.</span><span class="at">min</span>)<span class="op">.</span><span class="fu">attr</span>(<span class="st">&#39;max&#39;</span><span class="op">,</span> d <span class="kw">=&gt;</span> d<span class="op">.</span><span class="at">max</span>)<span class="op">.</span><span class="fu">attr</span>(<span class="st">&#39;step&#39;</span><span class="op">,</span> d <span class="kw">=&gt;</span> d<span class="op">.</span><span class="at">step</span>)</span> <span id="cb6-2753"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;align-self&#39;</span><span class="op">,</span> <span class="st">&#39;center&#39;</span>)</span>
<span id="cb6-2754"><a href></a> <span class="op">.</span><span class="fu">property</span>(<span class="st">&#39;value&#39;</span><span class="op">,</span> d <span class="kw">=&gt;</span> d<span class="op">.</span><span class="fu">get</span>())</span> <span id="cb6-2754"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;margin-left&#39;</span><span class="op">,</span> <span class="st">&#39;auto&#39;</span>)</span>
<span id="cb6-2755"><a href></a> <span class="op">.</span><span class="fu">on</span>(<span class="st">&#39;input&#39;</span><span class="op">,</span> <span class="kw">function</span>(<span class="bu">event</span><span class="op">,</span> d) {</span> <span id="cb6-2755"><a href></a> <span class="op">.</span><span class="fu">on</span>(<span class="st">&#39;click&#39;</span><span class="op">,</span> () <span class="kw">=&gt;</span> {</span>
<span id="cb6-2756"><a href></a> <span class="kw">const</span> val <span class="op">=</span> <span class="op">+</span><span class="kw">this</span><span class="op">.</span><span class="at">value</span><span class="op">;</span> d<span class="op">.</span><span class="fu">set</span>(val)<span class="op">;</span></span> <span id="cb6-2756"><a href></a> <span class="co">// reset state vars</span></span>
<span id="cb6-2757"><a href></a> d3<span class="op">.</span><span class="fu">select</span>(<span class="kw">this</span><span class="op">.</span><span class="at">parentNode</span>)<span class="op">.</span><span class="fu">select</span>(<span class="st">&#39;span&#39;</span>)<span class="op">.</span><span class="fu">text</span>(d<span class="op">.</span><span class="at">label</span><span class="op">.</span><span class="fu">match</span>(<span class="ss">/Sigma</span><span class="sc">|</span><span class="ss">Tailweight/</span>) <span class="op">?</span> <span class="dv">2</span><span class="op">**</span>val <span class="op">:</span> val)<span class="op">;</span></span> <span id="cb6-2757"><a href></a> selectedMu <span class="op">=</span> <span class="fl">0.5</span><span class="op">;</span></span>
<span id="cb6-2758"><a href></a> <span class="fu">updateChart</span>(<span class="fu">filteredData</span>())<span class="op">;</span></span> <span id="cb6-2758"><a href></a> selectedSig <span class="op">=</span> <span class="dv">1</span><span class="op">;</span></span>
<span id="cb6-2759"><a href></a> })</span> <span id="cb6-2759"><a href></a> selectedNonc <span class="op">=</span> <span class="dv">0</span><span class="op">;</span></span>
<span id="cb6-2760"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;width&#39;</span><span class="op">,</span> <span class="st">&#39;100%&#39;</span>)<span class="op">;</span></span> <span id="cb6-2760"><a href></a> selectedTailw <span class="op">=</span> <span class="dv">1</span><span class="op">;</span></span>
<span id="cb6-2761"><a href></a> sliderCont<span class="op">.</span><span class="fu">append</span>(<span class="st">&#39;span&#39;</span>)<span class="op">.</span><span class="fu">text</span>(d <span class="kw">=&gt;</span> (d<span class="op">.</span><span class="at">label</span><span class="op">.</span><span class="fu">match</span>(<span class="ss">/Sigma</span><span class="sc">|</span><span class="ss">Tailweight/</span>) <span class="op">?</span> d<span class="op">.</span><span class="fu">get</span>() <span class="op">:</span> d<span class="op">.</span><span class="fu">get</span>()))</span> <span id="cb6-2761"><a href></a> <span class="co">// update input positions</span></span>
<span id="cb6-2762"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;font-size&#39;</span><span class="op">,</span><span class="st">&#39;20px&#39;</span>)<span class="op">;</span></span> <span id="cb6-2762"><a href></a> sliderCont<span class="op">.</span><span class="fu">selectAll</span>(<span class="st">&#39;input&#39;</span>)<span class="op">.</span><span class="fu">property</span>(<span class="st">&#39;value&#39;</span><span class="op">,</span> d <span class="kw">=&gt;</span> d<span class="op">.</span><span class="fu">get</span>())<span class="op">;</span></span>
<span id="cb6-2763"><a href></a> </span> <span id="cb6-2763"><a href></a> <span class="co">// update displayed labels</span></span>
<span id="cb6-2764"><a href></a> <span class="co">// Add Reset button to clear all sliders to their defaults</span></span> <span id="cb6-2764"><a href></a> sliderCont<span class="op">.</span><span class="fu">selectAll</span>(<span class="st">&#39;span&#39;</span>)</span>
<span id="cb6-2765"><a href></a> controlsContainer<span class="op">.</span><span class="fu">append</span>(<span class="st">&#39;button&#39;</span>)</span> <span id="cb6-2765"><a href></a> <span class="op">.</span><span class="fu">text</span>(d <span class="kw">=&gt;</span> d<span class="op">.</span><span class="at">label</span><span class="op">.</span><span class="fu">match</span>(<span class="ss">/Sigma</span><span class="sc">|</span><span class="ss">Tailweight/</span>) <span class="op">?</span> (<span class="dv">2</span><span class="op">**</span>d<span class="op">.</span><span class="fu">get</span>()) <span class="op">:</span> d<span class="op">.</span><span class="fu">get</span>())<span class="op">;</span></span>
<span id="cb6-2766"><a href></a> <span class="op">.</span><span class="fu">text</span>(<span class="st">&#39;Reset&#39;</span>)</span> <span id="cb6-2766"><a href></a> <span class="co">// redraw chart</span></span>
<span id="cb6-2767"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;font-size&#39;</span><span class="op">,</span> <span class="st">&#39;20px&#39;</span>)</span> <span id="cb6-2767"><a href></a> <span class="fu">updateChart</span>(<span class="fu">filteredData</span>())<span class="op">;</span></span>
<span id="cb6-2768"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;align-self&#39;</span><span class="op">,</span> <span class="st">&#39;center&#39;</span>)</span> <span id="cb6-2768"><a href></a> })<span class="op">;</span></span>
<span id="cb6-2769"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&#39;margin-left&#39;</span><span class="op">,</span> <span class="st">&#39;auto&#39;</span>)</span> <span id="cb6-2769"><a href></a></span>
<span id="cb6-2770"><a href></a> <span class="op">.</span><span class="fu">on</span>(<span class="st">&#39;click&#39;</span><span class="op">,</span> () <span class="kw">=&gt;</span> {</span> <span id="cb6-2770"><a href></a> <span class="co">// Build SVG</span></span>
<span id="cb6-2771"><a href></a> <span class="co">// reset state vars</span></span> <span id="cb6-2771"><a href></a> <span class="kw">const</span> width <span class="op">=</span> <span class="dv">1200</span><span class="op">;</span></span>
<span id="cb6-2772"><a href></a> selectedMu <span class="op">=</span> <span class="fl">0.5</span><span class="op">;</span></span> <span id="cb6-2772"><a href></a> <span class="kw">const</span> height <span class="op">=</span> <span class="dv">450</span><span class="op">;</span></span>
<span id="cb6-2773"><a href></a> selectedSig <span class="op">=</span> <span class="dv">1</span><span class="op">;</span></span> <span id="cb6-2773"><a href></a> <span class="kw">const</span> margin <span class="op">=</span> {<span class="dt">top</span><span class="op">:</span> <span class="dv">40</span><span class="op">,</span> <span class="dt">right</span><span class="op">:</span> <span class="dv">20</span><span class="op">,</span> <span class="dt">bottom</span><span class="op">:</span> <span class="dv">40</span><span class="op">,</span> <span class="dt">left</span><span class="op">:</span> <span class="dv">40</span>}<span class="op">;</span></span>
<span id="cb6-2774"><a href></a> selectedNonc <span class="op">=</span> <span class="dv">0</span><span class="op">;</span></span> <span id="cb6-2774"><a href></a> <span class="kw">const</span> innerWidth <span class="op">=</span> width <span class="op">-</span> margin<span class="op">.</span><span class="at">left</span> <span class="op">-</span> margin<span class="op">.</span><span class="at">right</span><span class="op">;</span></span>
<span id="cb6-2775"><a href></a> selectedTailw <span class="op">=</span> <span class="dv">1</span><span class="op">;</span></span> <span id="cb6-2775"><a href></a> <span class="kw">const</span> innerHeight <span class="op">=</span> height <span class="op">-</span> margin<span class="op">.</span><span class="at">top</span> <span class="op">-</span> margin<span class="op">.</span><span class="at">bottom</span><span class="op">;</span></span>
<span id="cb6-2776"><a href></a> <span class="co">// update input positions</span></span> <span id="cb6-2776"><a href></a></span>
<span id="cb6-2777"><a href></a> sliderCont<span class="op">.</span><span class="fu">selectAll</span>(<span class="st">&#39;input&#39;</span>)<span class="op">.</span><span class="fu">property</span>(<span class="st">&#39;value&#39;</span><span class="op">,</span> d <span class="kw">=&gt;</span> d<span class="op">.</span><span class="fu">get</span>())<span class="op">;</span></span> <span id="cb6-2777"><a href></a> <span class="co">// Set controls container width to match SVG plot width</span></span>
<span id="cb6-2778"><a href></a> <span class="co">// update displayed labels</span></span> <span id="cb6-2778"><a href></a> controlsContainer<span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;max-width&quot;</span><span class="op">,</span> <span class="st">&quot;none&quot;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;width&quot;</span><span class="op">,</span> <span class="st">&quot;100%&quot;</span>)<span class="op">;</span></span>
<span id="cb6-2779"><a href></a> sliderCont<span class="op">.</span><span class="fu">selectAll</span>(<span class="st">&#39;span&#39;</span>)</span> <span id="cb6-2779"><a href></a> <span class="co">// Distribute each control evenly and make sliders full-width</span></span>
<span id="cb6-2780"><a href></a> <span class="op">.</span><span class="fu">text</span>(d <span class="kw">=&gt;</span> d<span class="op">.</span><span class="at">label</span><span class="op">.</span><span class="fu">match</span>(<span class="ss">/Sigma</span><span class="sc">|</span><span class="ss">Tailweight/</span>) <span class="op">?</span> (<span class="dv">2</span><span class="op">**</span>d<span class="op">.</span><span class="fu">get</span>()) <span class="op">:</span> d<span class="op">.</span><span class="fu">get</span>())<span class="op">;</span></span> <span id="cb6-2780"><a href></a> controlsContainer<span class="op">.</span><span class="fu">selectAll</span>(<span class="st">&quot;div&quot;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;flex&quot;</span><span class="op">,</span> <span class="st">&quot;1&quot;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;min-width&quot;</span><span class="op">,</span> <span class="st">&quot;0px&quot;</span>)<span class="op">;</span></span>
<span id="cb6-2781"><a href></a> <span class="co">// redraw chart</span></span> <span id="cb6-2781"><a href></a> controlsContainer<span class="op">.</span><span class="fu">selectAll</span>(<span class="st">&quot;input&quot;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;width&quot;</span><span class="op">,</span> <span class="st">&quot;100%&quot;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;box-sizing&quot;</span><span class="op">,</span> <span class="st">&quot;border-box&quot;</span>)<span class="op">;</span></span>
<span id="cb6-2782"><a href></a> <span class="fu">updateChart</span>(<span class="fu">filteredData</span>())<span class="op">;</span></span> <span id="cb6-2782"><a href></a> </span>
<span id="cb6-2783"><a href></a> })<span class="op">;</span></span> <span id="cb6-2783"><a href></a> <span class="co">// Create scales</span></span>
<span id="cb6-2784"><a href></a></span> <span id="cb6-2784"><a href></a> <span class="kw">const</span> x <span class="op">=</span> d3<span class="op">.</span><span class="fu">scaleLinear</span>()</span>
<span id="cb6-2785"><a href></a> <span class="co">// Build SVG</span></span> <span id="cb6-2785"><a href></a> <span class="op">.</span><span class="fu">domain</span>([<span class="dv">0</span><span class="op">,</span> <span class="dv">1</span>])</span>
<span id="cb6-2786"><a href></a> <span class="kw">const</span> width <span class="op">=</span> <span class="dv">1200</span><span class="op">;</span></span> <span id="cb6-2786"><a href></a> <span class="op">.</span><span class="fu">range</span>([<span class="dv">0</span><span class="op">,</span> innerWidth])<span class="op">;</span></span>
<span id="cb6-2787"><a href></a> <span class="kw">const</span> height <span class="op">=</span> <span class="dv">450</span><span class="op">;</span></span> <span id="cb6-2787"><a href></a> </span>
<span id="cb6-2788"><a href></a> <span class="kw">const</span> margin <span class="op">=</span> {<span class="dt">top</span><span class="op">:</span> <span class="dv">40</span><span class="op">,</span> <span class="dt">right</span><span class="op">:</span> <span class="dv">20</span><span class="op">,</span> <span class="dt">bottom</span><span class="op">:</span> <span class="dv">40</span><span class="op">,</span> <span class="dt">left</span><span class="op">:</span> <span class="dv">40</span>}<span class="op">;</span></span> <span id="cb6-2788"><a href></a> <span class="kw">const</span> y <span class="op">=</span> d3<span class="op">.</span><span class="fu">scaleLinear</span>()</span>
<span id="cb6-2789"><a href></a> <span class="kw">const</span> innerWidth <span class="op">=</span> width <span class="op">-</span> margin<span class="op">.</span><span class="at">left</span> <span class="op">-</span> margin<span class="op">.</span><span class="at">right</span><span class="op">;</span></span> <span id="cb6-2789"><a href></a> <span class="op">.</span><span class="fu">domain</span>([<span class="dv">0</span><span class="op">,</span> <span class="dv">1</span>])</span>
<span id="cb6-2790"><a href></a> <span class="kw">const</span> innerHeight <span class="op">=</span> height <span class="op">-</span> margin<span class="op">.</span><span class="at">top</span> <span class="op">-</span> margin<span class="op">.</span><span class="at">bottom</span><span class="op">;</span></span> <span id="cb6-2790"><a href></a> <span class="op">.</span><span class="fu">range</span>([innerHeight<span class="op">,</span> <span class="dv">0</span>])<span class="op">;</span></span>
<span id="cb6-2791"><a href></a></span> <span id="cb6-2791"><a href></a> </span>
<span id="cb6-2792"><a href></a> <span class="co">// Set controls container width to match SVG plot width</span></span> <span id="cb6-2792"><a href></a> <span class="co">// Create a color scale for the basis functions</span></span>
<span id="cb6-2793"><a href></a> controlsContainer<span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;max-width&quot;</span><span class="op">,</span> <span class="st">&quot;none&quot;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;width&quot;</span><span class="op">,</span> <span class="st">&quot;100%&quot;</span>)<span class="op">;</span></span> <span id="cb6-2793"><a href></a> <span class="kw">const</span> color <span class="op">=</span> d3<span class="op">.</span><span class="fu">scaleOrdinal</span>(d3<span class="op">.</span><span class="at">schemeCategory10</span>)<span class="op">;</span></span>
<span id="cb6-2794"><a href></a> <span class="co">// Distribute each control evenly and make sliders full-width</span></span> <span id="cb6-2794"><a href></a> </span>
<span id="cb6-2795"><a href></a> controlsContainer<span class="op">.</span><span class="fu">selectAll</span>(<span class="st">&quot;div&quot;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;flex&quot;</span><span class="op">,</span> <span class="st">&quot;1&quot;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;min-width&quot;</span><span class="op">,</span> <span class="st">&quot;0px&quot;</span>)<span class="op">;</span></span> <span id="cb6-2795"><a href></a> <span class="co">// Create SVG</span></span>
<span id="cb6-2796"><a href></a> controlsContainer<span class="op">.</span><span class="fu">selectAll</span>(<span class="st">&quot;input&quot;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;width&quot;</span><span class="op">,</span> <span class="st">&quot;100%&quot;</span>)<span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;box-sizing&quot;</span><span class="op">,</span> <span class="st">&quot;border-box&quot;</span>)<span class="op">;</span></span> <span id="cb6-2796"><a href></a> <span class="kw">const</span> svg <span class="op">=</span> d3<span class="op">.</span><span class="fu">create</span>(<span class="st">&quot;svg&quot;</span>)</span>
<span id="cb6-2797"><a href></a> </span> <span id="cb6-2797"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;width&quot;</span><span class="op">,</span> <span class="st">&quot;100%&quot;</span>)</span>
<span id="cb6-2798"><a href></a> <span class="co">// Create scales</span></span> <span id="cb6-2798"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;height&quot;</span><span class="op">,</span> <span class="st">&quot;auto&quot;</span>)</span>
<span id="cb6-2799"><a href></a> <span class="kw">const</span> x <span class="op">=</span> d3<span class="op">.</span><span class="fu">scaleLinear</span>()</span> <span id="cb6-2799"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;viewBox&quot;</span><span class="op">,</span> [<span class="dv">0</span><span class="op">,</span> <span class="dv">0</span><span class="op">,</span> width<span class="op">,</span> height])</span>
<span id="cb6-2800"><a href></a> <span class="op">.</span><span class="fu">domain</span>([<span class="dv">0</span><span class="op">,</span> <span class="dv">1</span>])</span> <span id="cb6-2800"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;preserveAspectRatio&quot;</span><span class="op">,</span> <span class="st">&quot;xMidYMid meet&quot;</span>)</span>
<span id="cb6-2801"><a href></a> <span class="op">.</span><span class="fu">range</span>([<span class="dv">0</span><span class="op">,</span> innerWidth])<span class="op">;</span></span> <span id="cb6-2801"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;style&quot;</span><span class="op">,</span> <span class="st">&quot;max-width: 100%; height: auto;&quot;</span>)<span class="op">;</span></span>
<span id="cb6-2802"><a href></a> </span> <span id="cb6-2802"><a href></a> </span>
<span id="cb6-2803"><a href></a> <span class="kw">const</span> y <span class="op">=</span> d3<span class="op">.</span><span class="fu">scaleLinear</span>()</span> <span id="cb6-2803"><a href></a> <span class="co">// Create the chart group</span></span>
<span id="cb6-2804"><a href></a> <span class="op">.</span><span class="fu">domain</span>([<span class="dv">0</span><span class="op">,</span> <span class="dv">1</span>])</span> <span id="cb6-2804"><a href></a> <span class="kw">const</span> g <span class="op">=</span> svg<span class="op">.</span><span class="fu">append</span>(<span class="st">&quot;g&quot;</span>)</span>
<span id="cb6-2805"><a href></a> <span class="op">.</span><span class="fu">range</span>([innerHeight<span class="op">,</span> <span class="dv">0</span>])<span class="op">;</span></span> <span id="cb6-2805"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;transform&quot;</span><span class="op">,</span> <span class="vs">`translate(</span><span class="sc">${</span>margin<span class="op">.</span><span class="at">left</span><span class="sc">}</span><span class="vs">,</span><span class="sc">${</span>margin<span class="op">.</span><span class="at">top</span><span class="sc">}</span><span class="vs">)`</span>)<span class="op">;</span></span>
<span id="cb6-2806"><a href></a> </span> <span id="cb6-2806"><a href></a> </span>
<span id="cb6-2807"><a href></a> <span class="co">// Create a color scale for the basis functions</span></span> <span id="cb6-2807"><a href></a> <span class="co">// Add axes</span></span>
<span id="cb6-2808"><a href></a> <span class="kw">const</span> color <span class="op">=</span> d3<span class="op">.</span><span class="fu">scaleOrdinal</span>(d3<span class="op">.</span><span class="at">schemeCategory10</span>)<span class="op">;</span></span> <span id="cb6-2808"><a href></a> <span class="kw">const</span> xAxis <span class="op">=</span> g<span class="op">.</span><span class="fu">append</span>(<span class="st">&quot;g&quot;</span>)</span>
<span id="cb6-2809"><a href></a> </span> <span id="cb6-2809"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;transform&quot;</span><span class="op">,</span> <span class="vs">`translate(0,</span><span class="sc">${</span>innerHeight<span class="sc">}</span><span class="vs">)`</span>)</span>
<span id="cb6-2810"><a href></a> <span class="co">// Create SVG</span></span> <span id="cb6-2810"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;class&quot;</span><span class="op">,</span> <span class="st">&quot;x-axis&quot;</span>)</span>
<span id="cb6-2811"><a href></a> <span class="kw">const</span> svg <span class="op">=</span> d3<span class="op">.</span><span class="fu">create</span>(<span class="st">&quot;svg&quot;</span>)</span> <span id="cb6-2811"><a href></a> <span class="op">.</span><span class="fu">call</span>(d3<span class="op">.</span><span class="fu">axisBottom</span>(x)<span class="op">.</span><span class="fu">ticks</span>(<span class="dv">10</span>))</span>
<span id="cb6-2812"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;width&quot;</span><span class="op">,</span> <span class="st">&quot;100%&quot;</span>)</span> <span id="cb6-2812"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;font-size&quot;</span><span class="op">,</span> <span class="st">&quot;20px&quot;</span>)<span class="op">;</span></span>
<span id="cb6-2813"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;height&quot;</span><span class="op">,</span> <span class="st">&quot;auto&quot;</span>)</span> <span id="cb6-2813"><a href></a> </span>
<span id="cb6-2814"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;viewBox&quot;</span><span class="op">,</span> [<span class="dv">0</span><span class="op">,</span> <span class="dv">0</span><span class="op">,</span> width<span class="op">,</span> height])</span> <span id="cb6-2814"><a href></a> <span class="kw">const</span> yAxis <span class="op">=</span> g<span class="op">.</span><span class="fu">append</span>(<span class="st">&quot;g&quot;</span>)</span>
<span id="cb6-2815"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;preserveAspectRatio&quot;</span><span class="op">,</span> <span class="st">&quot;xMidYMid meet&quot;</span>)</span> <span id="cb6-2815"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;class&quot;</span><span class="op">,</span> <span class="st">&quot;y-axis&quot;</span>)</span>
<span id="cb6-2816"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;style&quot;</span><span class="op">,</span> <span class="st">&quot;max-width: 100%; height: auto;&quot;</span>)<span class="op">;</span></span> <span id="cb6-2816"><a href></a> <span class="op">.</span><span class="fu">call</span>(d3<span class="op">.</span><span class="fu">axisLeft</span>(y)<span class="op">.</span><span class="fu">ticks</span>(<span class="dv">5</span>))</span>
<span id="cb6-2817"><a href></a> </span> <span id="cb6-2817"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;font-size&quot;</span><span class="op">,</span> <span class="st">&quot;20px&quot;</span>)<span class="op">;</span></span>
<span id="cb6-2818"><a href></a> <span class="co">// Create the chart group</span></span> <span id="cb6-2818"><a href></a> </span>
<span id="cb6-2819"><a href></a> <span class="kw">const</span> g <span class="op">=</span> svg<span class="op">.</span><span class="fu">append</span>(<span class="st">&quot;g&quot;</span>)</span> <span id="cb6-2819"><a href></a> <span class="co">// Add a horizontal line at y = 0</span></span>
<span id="cb6-2820"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;transform&quot;</span><span class="op">,</span> <span class="vs">`translate(</span><span class="sc">${</span>margin<span class="op">.</span><span class="at">left</span><span class="sc">}</span><span class="vs">,</span><span class="sc">${</span>margin<span class="op">.</span><span class="at">top</span><span class="sc">}</span><span class="vs">)`</span>)<span class="op">;</span></span> <span id="cb6-2820"><a href></a> g<span class="op">.</span><span class="fu">append</span>(<span class="st">&quot;line&quot;</span>)</span>
<span id="cb6-2821"><a href></a> </span> <span id="cb6-2821"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;x1&quot;</span><span class="op">,</span> <span class="dv">0</span>)</span>
<span id="cb6-2822"><a href></a> <span class="co">// Add axes</span></span> <span id="cb6-2822"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;x2&quot;</span><span class="op">,</span> innerWidth)</span>
<span id="cb6-2823"><a href></a> <span class="kw">const</span> xAxis <span class="op">=</span> g<span class="op">.</span><span class="fu">append</span>(<span class="st">&quot;g&quot;</span>)</span> <span id="cb6-2823"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;y1&quot;</span><span class="op">,</span> <span class="fu">y</span>(<span class="dv">0</span>))</span>
<span id="cb6-2824"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;transform&quot;</span><span class="op">,</span> <span class="vs">`translate(0,</span><span class="sc">${</span>innerHeight<span class="sc">}</span><span class="vs">)`</span>)</span> <span id="cb6-2824"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;y2&quot;</span><span class="op">,</span> <span class="fu">y</span>(<span class="dv">0</span>))</span>
<span id="cb6-2825"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;class&quot;</span><span class="op">,</span> <span class="st">&quot;x-axis&quot;</span>)</span> <span id="cb6-2825"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;stroke&quot;</span><span class="op">,</span> <span class="st">&quot;#000&quot;</span>)</span>
<span id="cb6-2826"><a href></a> <span class="op">.</span><span class="fu">call</span>(d3<span class="op">.</span><span class="fu">axisBottom</span>(x)<span class="op">.</span><span class="fu">ticks</span>(<span class="dv">10</span>))</span> <span id="cb6-2826"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;stroke-opacity&quot;</span><span class="op">,</span> <span class="fl">0.2</span>)<span class="op">;</span></span>
<span id="cb6-2827"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;font-size&quot;</span><span class="op">,</span> <span class="st">&quot;20px&quot;</span>)<span class="op">;</span></span> <span id="cb6-2827"><a href></a> </span>
<span id="cb6-2828"><a href></a> </span> <span id="cb6-2828"><a href></a> <span class="co">// Add gridlines</span></span>
<span id="cb6-2829"><a href></a> <span class="kw">const</span> yAxis <span class="op">=</span> g<span class="op">.</span><span class="fu">append</span>(<span class="st">&quot;g&quot;</span>)</span> <span id="cb6-2829"><a href></a> g<span class="op">.</span><span class="fu">append</span>(<span class="st">&quot;g&quot;</span>)</span>
<span id="cb6-2830"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;class&quot;</span><span class="op">,</span> <span class="st">&quot;y-axis&quot;</span>)</span> <span id="cb6-2830"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;class&quot;</span><span class="op">,</span> <span class="st">&quot;grid-lines&quot;</span>)</span>
<span id="cb6-2831"><a href></a> <span class="op">.</span><span class="fu">call</span>(d3<span class="op">.</span><span class="fu">axisLeft</span>(y)<span class="op">.</span><span class="fu">ticks</span>(<span class="dv">5</span>))</span> <span id="cb6-2831"><a href></a> <span class="op">.</span><span class="fu">selectAll</span>(<span class="st">&quot;line&quot;</span>)</span>
<span id="cb6-2832"><a href></a> <span class="op">.</span><span class="fu">style</span>(<span class="st">&quot;font-size&quot;</span><span class="op">,</span> <span class="st">&quot;20px&quot;</span>)<span class="op">;</span></span> <span id="cb6-2832"><a href></a> <span class="op">.</span><span class="fu">data</span>(y<span class="op">.</span><span class="fu">ticks</span>(<span class="dv">5</span>))</span>
<span id="cb6-2833"><a href></a> </span> <span id="cb6-2833"><a href></a> <span class="op">.</span><span class="fu">join</span>(<span class="st">&quot;line&quot;</span>)</span>
<span id="cb6-2834"><a href></a> <span class="co">// Add a horizontal line at y = 0</span></span> <span id="cb6-2834"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;x1&quot;</span><span class="op">,</span> <span class="dv">0</span>)</span>
<span id="cb6-2835"><a href></a> g<span class="op">.</span><span class="fu">append</span>(<span class="st">&quot;line&quot;</span>)</span> <span id="cb6-2835"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;x2&quot;</span><span class="op">,</span> innerWidth)</span>
<span id="cb6-2836"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;x1&quot;</span><span class="op">,</span> <span class="dv">0</span>)</span> <span id="cb6-2836"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;y1&quot;</span><span class="op">,</span> d <span class="kw">=&gt;</span> <span class="fu">y</span>(d))</span>
<span id="cb6-2837"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;x2&quot;</span><span class="op">,</span> innerWidth)</span> <span id="cb6-2837"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;y2&quot;</span><span class="op">,</span> d <span class="kw">=&gt;</span> <span class="fu">y</span>(d))</span>
<span id="cb6-2838"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;y1&quot;</span><span class="op">,</span> <span class="fu">y</span>(<span class="dv">0</span>))</span> <span id="cb6-2838"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;stroke&quot;</span><span class="op">,</span> <span class="st">&quot;#ccc&quot;</span>)</span>
<span id="cb6-2839"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;y2&quot;</span><span class="op">,</span> <span class="fu">y</span>(<span class="dv">0</span>))</span> <span id="cb6-2839"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;stroke-opacity&quot;</span><span class="op">,</span> <span class="fl">0.5</span>)<span class="op">;</span></span>
<span id="cb6-2840"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;stroke&quot;</span><span class="op">,</span> <span class="st">&quot;#000&quot;</span>)</span> <span id="cb6-2840"><a href></a> </span>
<span id="cb6-2841"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;stroke-opacity&quot;</span><span class="op">,</span> <span class="fl">0.2</span>)<span class="op">;</span></span> <span id="cb6-2841"><a href></a> <span class="co">// Create a line generator</span></span>
<span id="cb6-2842"><a href></a> </span> <span id="cb6-2842"><a href></a> <span class="kw">const</span> line <span class="op">=</span> d3<span class="op">.</span><span class="fu">line</span>()</span>
<span id="cb6-2843"><a href></a> <span class="co">// Add gridlines</span></span> <span id="cb6-2843"><a href></a> <span class="op">.</span><span class="fu">x</span>(d <span class="kw">=&gt;</span> <span class="fu">x</span>(d<span class="op">.</span><span class="at">x</span>))</span>
<span id="cb6-2844"><a href></a> g<span class="op">.</span><span class="fu">append</span>(<span class="st">&quot;g&quot;</span>)</span> <span id="cb6-2844"><a href></a> <span class="op">.</span><span class="fu">y</span>(d <span class="kw">=&gt;</span> <span class="fu">y</span>(d<span class="op">.</span><span class="at">y</span>))</span>
<span id="cb6-2845"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;class&quot;</span><span class="op">,</span> <span class="st">&quot;grid-lines&quot;</span>)</span> <span id="cb6-2845"><a href></a> <span class="op">.</span><span class="fu">curve</span>(d3<span class="op">.</span><span class="at">curveBasis</span>)<span class="op">;</span></span>
<span id="cb6-2846"><a href></a> <span class="op">.</span><span class="fu">selectAll</span>(<span class="st">&quot;line&quot;</span>)</span> <span id="cb6-2846"><a href></a> </span>
<span id="cb6-2847"><a href></a> <span class="op">.</span><span class="fu">data</span>(y<span class="op">.</span><span class="fu">ticks</span>(<span class="dv">5</span>))</span> <span id="cb6-2847"><a href></a> <span class="co">// Group to contain the basis function lines</span></span>
<span id="cb6-2848"><a href></a> <span class="op">.</span><span class="fu">join</span>(<span class="st">&quot;line&quot;</span>)</span> <span id="cb6-2848"><a href></a> <span class="kw">const</span> linesGroup <span class="op">=</span> g<span class="op">.</span><span class="fu">append</span>(<span class="st">&quot;g&quot;</span>)</span>
<span id="cb6-2849"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;x1&quot;</span><span class="op">,</span> <span class="dv">0</span>)</span> <span id="cb6-2849"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;class&quot;</span><span class="op">,</span> <span class="st">&quot;basis-functions&quot;</span>)<span class="op">;</span></span>
<span id="cb6-2850"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;x2&quot;</span><span class="op">,</span> innerWidth)</span> <span id="cb6-2850"><a href></a> </span>
<span id="cb6-2851"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;y1&quot;</span><span class="op">,</span> d <span class="kw">=&gt;</span> <span class="fu">y</span>(d))</span> <span id="cb6-2851"><a href></a> <span class="co">// Store the current basis functions for transition</span></span>
<span id="cb6-2852"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;y2&quot;</span><span class="op">,</span> d <span class="kw">=&gt;</span> <span class="fu">y</span>(d))</span> <span id="cb6-2852"><a href></a> <span class="kw">let</span> currentBasisFunctions <span class="op">=</span> <span class="kw">new</span> <span class="bu">Map</span>()<span class="op">;</span></span>
<span id="cb6-2853"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;stroke&quot;</span><span class="op">,</span> <span class="st">&quot;#ccc&quot;</span>)</span> <span id="cb6-2853"><a href></a> </span>
<span id="cb6-2854"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;stroke-opacity&quot;</span><span class="op">,</span> <span class="fl">0.5</span>)<span class="op">;</span></span> <span id="cb6-2854"><a href></a> <span class="co">// Function to update the chart with new data</span></span>
<span id="cb6-2855"><a href></a> </span> <span id="cb6-2855"><a href></a> <span class="kw">function</span> <span class="fu">updateChart</span>(data) {</span>
<span id="cb6-2856"><a href></a> <span class="co">// Create a line generator</span></span> <span id="cb6-2856"><a href></a> <span class="fu">updateChartInner</span>(g<span class="op">,</span> x<span class="op">,</span> y<span class="op">,</span> linesGroup<span class="op">,</span> color<span class="op">,</span> line<span class="op">,</span> data)<span class="op">;</span></span>
<span id="cb6-2857"><a href></a> <span class="kw">const</span> line <span class="op">=</span> d3<span class="op">.</span><span class="fu">line</span>()</span> <span id="cb6-2857"><a href></a> }</span>
<span id="cb6-2858"><a href></a> <span class="op">.</span><span class="fu">x</span>(d <span class="kw">=&gt;</span> <span class="fu">x</span>(d<span class="op">.</span><span class="at">x</span>))</span> <span id="cb6-2858"><a href></a> </span>
<span id="cb6-2859"><a href></a> <span class="op">.</span><span class="fu">y</span>(d <span class="kw">=&gt;</span> <span class="fu">y</span>(d<span class="op">.</span><span class="at">y</span>))</span> <span id="cb6-2859"><a href></a> <span class="co">// Store the update function</span></span>
<span id="cb6-2860"><a href></a> <span class="op">.</span><span class="fu">curve</span>(d3<span class="op">.</span><span class="at">curveBasis</span>)<span class="op">;</span></span> <span id="cb6-2860"><a href></a> svg<span class="op">.</span><span class="fu">node</span>()<span class="op">.</span><span class="at">update</span> <span class="op">=</span> updateChart<span class="op">;</span></span>
<span id="cb6-2861"><a href></a> </span> <span id="cb6-2861"><a href></a> </span>
<span id="cb6-2862"><a href></a> <span class="co">// Group to contain the basis function lines</span></span> <span id="cb6-2862"><a href></a> <span class="co">// Initial render</span></span>
<span id="cb6-2863"><a href></a> <span class="kw">const</span> linesGroup <span class="op">=</span> g<span class="op">.</span><span class="fu">append</span>(<span class="st">&quot;g&quot;</span>)</span> <span id="cb6-2863"><a href></a> <span class="fu">updateChart</span>(<span class="fu">filteredData</span>())<span class="op">;</span></span>
<span id="cb6-2864"><a href></a> <span class="op">.</span><span class="fu">attr</span>(<span class="st">&quot;class&quot;</span><span class="op">,</span> <span class="st">&quot;basis-functions&quot;</span>)<span class="op">;</span></span> <span id="cb6-2864"><a href></a> </span>
<span id="cb6-2865"><a href></a> </span> <span id="cb6-2865"><a href></a> container<span class="op">.</span><span class="fu">node</span>()<span class="op">.</span><span class="fu">appendChild</span>(svg<span class="op">.</span><span class="fu">node</span>())<span class="op">;</span></span>
<span id="cb6-2866"><a href></a> <span class="co">// Store the current basis functions for transition</span></span> <span id="cb6-2866"><a href></a> <span class="cf">return</span> container<span class="op">.</span><span class="fu">node</span>()<span class="op">;</span></span>
<span id="cb6-2867"><a href></a> <span class="kw">let</span> currentBasisFunctions <span class="op">=</span> <span class="kw">new</span> <span class="bu">Map</span>()<span class="op">;</span></span> <span id="cb6-2867"><a href></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<span id="cb6-2868"><a href></a> </span>
<span id="cb6-2869"><a href></a> <span class="co">// Function to update the chart with new data</span></span>
<span id="cb6-2870"><a href></a> <span class="kw">function</span> <span class="fu">updateChart</span>(data) {</span>
<span id="cb6-2871"><a href></a> <span class="fu">updateChartInner</span>(g<span class="op">,</span> x<span class="op">,</span> y<span class="op">,</span> linesGroup<span class="op">,</span> color<span class="op">,</span> line<span class="op">,</span> data)<span class="op">;</span></span>
<span id="cb6-2872"><a href></a> }</span>
<span id="cb6-2873"><a href></a> </span>
<span id="cb6-2874"><a href></a> <span class="co">// Store the update function</span></span>
<span id="cb6-2875"><a href></a> svg<span class="op">.</span><span class="fu">node</span>()<span class="op">.</span><span class="at">update</span> <span class="op">=</span> updateChart<span class="op">;</span></span>
<span id="cb6-2876"><a href></a> </span>
<span id="cb6-2877"><a href></a> <span class="co">// Initial render</span></span>
<span id="cb6-2878"><a href></a> <span class="fu">updateChart</span>(<span class="fu">filteredData</span>())<span class="op">;</span></span>
<span id="cb6-2879"><a href></a> </span>
<span id="cb6-2880"><a href></a> container<span class="op">.</span><span class="fu">node</span>()<span class="op">.</span><span class="fu">appendChild</span>(svg<span class="op">.</span><span class="fu">node</span>())<span class="op">;</span></span>
<span id="cb6-2881"><a href></a> <span class="cf">return</span> container<span class="op">.</span><span class="fu">node</span>()<span class="op">;</span></span>
<span id="cb6-2882"><a href></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display"> <div class="cell-output cell-output-display">
<div id="ojs-cell-5" data-nodetype="declaration"> <div id="ojs-cell-5" data-nodetype="declaration">
@@ -27529,7 +27523,7 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \
<div class="columns"> <div class="columns">
<div class="column" style="width:48%;"> <div class="column" style="width:48%;">
<h3 id="motivation-1">Motivation</h3> <h3 id="motivation-1">Motivation</h3>
<p>Understanding European Allowances (EUA) dynamics is important for several fields:</p> <p>Understanding European Emission Allowances (EUA)</p>
<p><i class="fa fa-fw fa-chart-pie" style="color:var(--col_grey_9);"></i> Portfolio &amp; Risk Management,</p> <p><i class="fa fa-fw fa-chart-pie" style="color:var(--col_grey_9);"></i> Portfolio &amp; Risk Management,</p>
<p><i class="fa fa-fw fa-timeline" style="color:var(--col_grey_9);"></i> Sustainability Planing</p> <p><i class="fa fa-fw fa-timeline" style="color:var(--col_grey_9);"></i> Sustainability Planing</p>
<p><i class="fa fa-fw fa-handshake" style="color:var(--col_grey_9);"></i> Political decisions</p> <p><i class="fa fa-fw fa-handshake" style="color:var(--col_grey_9);"></i> Political decisions</p>
@@ -27607,8 +27601,9 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \
<p><span class="math display">\[\mathbf{F} = (F_1, \ldots, F_K)^{\intercal}\]</span></p> <p><span class="math display">\[\mathbf{F} = (F_1, \ldots, F_K)^{\intercal}\]</span></p>
<p>Generalized non-central t-distributions</p> <p>Generalized non-central t-distributions</p>
<ul> <ul>
<li>Time varying: expectation <span class="math inline">\(\boldsymbol{\mu}_t = (\mu_{1,t}, \ldots, \mu_{K,t})^{\intercal}\)</span> <li>Time varying:
<ul> <ul>
<li>expectation <span class="math inline">\(\boldsymbol{\mu}_t = (\mu_{1,t}, \ldots, \mu_{K,t})^{\intercal}\)</span></li>
<li>variance: <span class="math inline">\(\boldsymbol{\sigma}_{t}^2 = (\sigma_{1,t}^2, \ldots, \sigma_{K,t}^2)^{\intercal}\)</span></li> <li>variance: <span class="math inline">\(\boldsymbol{\sigma}_{t}^2 = (\sigma_{1,t}^2, \ldots, \sigma_{K,t}^2)^{\intercal}\)</span></li>
</ul></li> </ul></li>
<li>Time invariant <li>Time invariant

33
index.qmd
View File

@@ -1041,39 +1041,24 @@ chart = {
### &nbsp; ### &nbsp;
:::: {.columns}
::: {.column width="48%"}
Each day, $t = 1, 2, ... T$ Each day, $t = 1, 2, ... T$
- The **forecaster** receives predictions $\widehat{X}_{t,k}$ from $K$ **experts** - The **forecaster** receives predictions $\widehat{X}_{t,k}$ from $K$ **experts**
- The **forecaster** assigns weights $w_{t,k}$ to each **expert** - The **forecaster** assigns weights $w_{t,k}$ to each **expert**
- The **forecaster** calculates her prediction: - The **forecaster** calculates the prediction:
\begin{equation} \begin{equation}
\widetilde{X}_{t} = \sum_{k=1}^K w_{t,k} \widehat{X}_{t,k}. \widetilde{X}_{t} = \sum_{k=1}^K w_{t,k} \widehat{X}_{t,k}.
\label{eq_forecast_def} \label{eq_forecast_def}
\end{equation} \end{equation}
- The realization for $t$ is observed - The realization for $t$ is observed
::: <i class="fa fa-fw fa-arrow-right" style="color:var(--col_grey_9);"></i> The experts can be institutions, persons, or models
::: {.column width="4%"} <i class="fa fa-fw fa-arrow-right" style="color:var(--col_grey_9);"></i> The forecasts can be point-forecasts (i.e., mean or median) or full predictive distributions
::: <i class="fa fa-fw fa-arrow-right" style="color:var(--col_grey_9);"></i> @cesa2006prediction
::: {.column width="48%"}
- The experts can be institutions, persons, or models
- The forecasts can be point-forecasts (i.e., mean or median) or full predictive distributions
- We do not need a distributional assumption concerning the underlying data
- @cesa2006prediction
:::
::::
---
## The Regret ## The Regret
@@ -3005,8 +2990,7 @@ Berrisch, J., Pappert, S., Ziel, F., & Arsova, A. (2023). *Finance Research Lett
### Motivation ### Motivation
Understanding European Allowances (EUA) dynamics is important Understanding European Emission Allowances (EUA)
for several fields:
<i class="fa fa-fw fa-chart-pie" style="color:var(--col_grey_9);"></i> Portfolio & Risk Management, <i class="fa fa-fw fa-chart-pie" style="color:var(--col_grey_9);"></i> Portfolio & Risk Management,
@@ -3179,7 +3163,8 @@ $$\mathbf{F} = (F_1, \ldots, F_K)^{\intercal}$$
Generalized non-central t-distributions Generalized non-central t-distributions
- Time varying: expectation $\boldsymbol{\mu}_t = (\mu_{1,t}, \ldots, \mu_{K,t})^{\intercal}$ - Time varying:
- expectation $\boldsymbol{\mu}_t = (\mu_{1,t}, \ldots, \mu_{K,t})^{\intercal}$
- variance: $\boldsymbol{\sigma}_{t}^2 = (\sigma_{1,t}^2, \ldots, \sigma_{K,t}^2)^{\intercal}$ - variance: $\boldsymbol{\sigma}_{t}^2 = (\sigma_{1,t}^2, \ldots, \sigma_{K,t}^2)^{\intercal}$
- Time invariant - Time invariant
- degrees of freedom: $\boldsymbol{\nu} = (\nu_1, \ldots, \nu_K)^{\intercal}$ - degrees of freedom: $\boldsymbol{\nu} = (\nu_1, \ldots, \nu_K)^{\intercal}$