Deploy preview for PR 119

Author: penelopeysm

pr-previews/119/index.html

@@ -442,7 +442,7 @@
 <div class="d-flex flex-row flex-wrap panel-wrapper gap-4 section-end-space">
 <section id="expressive" class="panel-title pb-1 panel">
 <h5 class="panel-title pb-1 anchored">Expressive</h5>
-<p>Turing models are easy to write and communicate — their syntax closely resembles mathematical notation.</p>
+<p>Turing models are easy to write and communicate.</p>
 </section>
 <section id="general-purpose" class="panel-title pb-1 panel">
 <h5 class="panel-title pb-1 anchored">General-purpose</h5>
@@ -519,39 +519,35 @@ <h5 class="panel-title pb-1 anchored">Composable</h5>
 <div class="fs-4 fw-bold pb-1">
 Composability with Julia
 </div>
-<p>As Turing.jl models are simply Julia functions under the hood, they can contain arbitrary Julia code.</p>
-<p>For example, <a href="https://turinglang.org/docs/tutorials/bayesian-differential-equations/">differential equations</a> can be added to a model using the <code>DifferentialEquations.jl</code> Julia package.</p>
+<p>As Turing.jl models are simply Julia functions under the hood, they can contain arbitrary Julia code. This allows users to draw on the rich numerical and scientific computing ecosystem of Julia.</p>
+<p>In the example here, we define an <a href="https://turinglang.org/docs/tutorials/bayesian-differential-equations/">ordinary differential equations</a> using the <code>DifferentialEquations.jl</code> Julia package and use it in a Turing.jl model.</p>
 </div>
 <div class="example-code" style="overflow-x: scroll;">
-<div class="sourceCode" id="cb4"><pre class="sourceCode julia code-overflow-scroll code-with-copy"><code class="sourceCode julia"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">DifferentialEquations</span></span>
-<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a><span class="co"># Define the system of equations</span></span>
-<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a><span class="kw">function</span> <span class="fu">lotka_volterra</span>(du, u, params, t)</span>
-<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a>    α, β, δ, γ <span class="op">=</span> params</span>
-<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a>    x, y <span class="op">=</span> u</span>
-<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a>    du[<span class="fl">1</span>] <span class="op">=</span> (α <span class="op">*</span> x) <span class="op">-</span> (β <span class="op">*</span> x <span class="op">*</span> y)</span>
-<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a>    du[<span class="fl">2</span>] <span class="op">=</span> (δ <span class="op">*</span> x <span class="op">*</span> y) <span class="op">-</span> (γ <span class="op">*</span> y)</span>
-<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a><span class="kw">end</span></span>
-<span id="cb4-10"><a href="#cb4-10" aria-hidden="true" tabindex="-1"></a>prob <span class="op">=</span> <span class="fu">ODEProblem</span>(lotka_volterra, <span class="op">...</span>)</span>
-<span id="cb4-11"><a href="#cb4-11" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb4-12"><a href="#cb4-12" aria-hidden="true" tabindex="-1"></a><span class="co"># Use it in a model</span></span>
-<span id="cb4-13"><a href="#cb4-13" aria-hidden="true" tabindex="-1"></a><span class="pp">@model</span> <span class="kw">function</span> <span class="fu">fit_lotka_volterra</span>()</span>
-<span id="cb4-14"><a href="#cb4-14" aria-hidden="true" tabindex="-1"></a>    <span class="co"># Priors</span></span>
-<span id="cb4-15"><a href="#cb4-15" aria-hidden="true" tabindex="-1"></a>    α <span class="op">~</span> <span class="fu">Normal</span>(<span class="fl">0</span>, <span class="fl">1</span>)</span>
-<span id="cb4-16"><a href="#cb4-16" aria-hidden="true" tabindex="-1"></a>    <span class="co"># ...</span></span>
-<span id="cb4-17"><a href="#cb4-17" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb4-18"><a href="#cb4-18" aria-hidden="true" tabindex="-1"></a>    <span class="co"># Solve the ODE</span></span>
-<span id="cb4-19"><a href="#cb4-19" aria-hidden="true" tabindex="-1"></a>    predictions <span class="op">=</span> <span class="fu">solve</span>(prob, <span class="fu">Tsit5</span>(); p<span class="op">=</span>p)</span>
-<span id="cb4-20"><a href="#cb4-20" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb4-21"><a href="#cb4-21" aria-hidden="true" tabindex="-1"></a>    <span class="co"># Likelihood</span></span>
-<span id="cb4-22"><a href="#cb4-22" aria-hidden="true" tabindex="-1"></a>    data <span class="op">~</span> <span class="fu">Poisson</span>.(predictions, <span class="op">...</span>)</span>
-<span id="cb4-23"><a href="#cb4-23" aria-hidden="true" tabindex="-1"></a><span class="kw">end</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode" id="cb4"><pre class="sourceCode julia code-overflow-scroll code-with-copy"><code class="sourceCode julia"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Define the system of equations</span></span>
+<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">DifferentialEquations</span></span>
+<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a><span class="kw">function</span> <span class="fu">lotka_volterra</span>(du, u, params, t)</span>
+<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a>    α, β, δ, γ <span class="op">=</span> params</span>
+<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a>    x, y <span class="op">=</span> u</span>
+<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a>    du[<span class="fl">1</span>] <span class="op">=</span> (α <span class="op">*</span> x) <span class="op">-</span> (β <span class="op">*</span> x <span class="op">*</span> y)</span>
+<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a>    du[<span class="fl">2</span>] <span class="op">=</span> (δ <span class="op">*</span> x <span class="op">*</span> y) <span class="op">-</span> (γ <span class="op">*</span> y)</span>
+<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a><span class="kw">end</span></span>
+<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a>prob <span class="op">=</span> <span class="fu">ODEProblem</span>(lotka_volterra, <span class="op">...</span>)</span>
+<span id="cb4-10"><a href="#cb4-10" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb4-11"><a href="#cb4-11" aria-hidden="true" tabindex="-1"></a><span class="co"># Use it in a model</span></span>
+<span id="cb4-12"><a href="#cb4-12" aria-hidden="true" tabindex="-1"></a><span class="pp">@model</span> <span class="kw">function</span> <span class="fu">fit_lotka_volterra</span>()</span>
+<span id="cb4-13"><a href="#cb4-13" aria-hidden="true" tabindex="-1"></a>    <span class="co"># Priors on ODE parameters</span></span>
+<span id="cb4-14"><a href="#cb4-14" aria-hidden="true" tabindex="-1"></a>    α <span class="op">~</span> <span class="fu">Normal</span>(<span class="fl">0</span>, <span class="fl">1</span>) <span class="co"># and others...</span></span>
+<span id="cb4-15"><a href="#cb4-15" aria-hidden="true" tabindex="-1"></a>    <span class="co"># Solve the ODE</span></span>
+<span id="cb4-16"><a href="#cb4-16" aria-hidden="true" tabindex="-1"></a>    predictions <span class="op">=</span> <span class="fu">solve</span>(prob, <span class="fu">Tsit5</span>(); params<span class="op">=</span>(α, <span class="op">...</span>))</span>
+<span id="cb4-17"><a href="#cb4-17" aria-hidden="true" tabindex="-1"></a>    <span class="co"># Calculate likelihood</span></span>
+<span id="cb4-18"><a href="#cb4-18" aria-hidden="true" tabindex="-1"></a>    data <span class="op">~</span> <span class="fu">Poisson</span>.(predictions, <span class="op">...</span>)</span>
+<span id="cb4-19"><a href="#cb4-19" aria-hidden="true" tabindex="-1"></a><span class="kw">end</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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