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Documenter.jl committed Nov 25, 2024
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2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-24T00:24:37","documenter_version":"1.8.0"}}
{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-25T00:23:03","documenter_version":"1.8.0"}}
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4 changes: 2 additions & 2 deletions dev/examples/initializing-hmc/index.html

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2,168 changes: 1,084 additions & 1,084 deletions dev/examples/quickstart/ae89033d.svg → dev/examples/quickstart/19b18f23.svg
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2,146 changes: 1,073 additions & 1,073 deletions dev/examples/quickstart/7c351ee5.svg → dev/examples/quickstart/413fa5d2.svg
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6 changes: 3 additions & 3 deletions dev/examples/quickstart/index.html
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prob_banana = BananaProblem()</code></pre><p>and then visualise it:</p><pre><code class="language-julia hljs">xrange = -3.5:0.05:3.5
yrange = -3:0.05:7
logp_banana(x) = LogDensityProblems.logdensity(prob_banana, x)
contour(xrange, yrange, exp ∘ logp_banana ∘ Base.vect; xlabel=&quot;x₁&quot;, ylabel=&quot;x₂&quot;)</code></pre><img src="430db631.svg" alt="Example block output"/><p>Now we run <a href="../../lib/public/#Pathfinder.pathfinder"><code>pathfinder</code></a>.</p><pre><code class="language-julia hljs">result = pathfinder(prob_banana; init_scale=10)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Single-path Pathfinder result
contour(xrange, yrange, exp ∘ logp_banana ∘ Base.vect; xlabel=&quot;x₁&quot;, ylabel=&quot;x₂&quot;)</code></pre><img src="28323b8d.svg" alt="Example block output"/><p>Now we run <a href="../../lib/public/#Pathfinder.pathfinder"><code>pathfinder</code></a>.</p><pre><code class="language-julia hljs">result = pathfinder(prob_banana; init_scale=10)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Single-path Pathfinder result
tries: 1
draws: 5
fit iteration: 10 (total: 17)
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contour(xrange, yrange, exp ∘ logp_banana ∘ Base.vect)
scatter!(x₁_approx, x₂_approx; msw=0, ms=2, alpha=0.5, color=1)
plot!(xlims=extrema(xrange), ylims=extrema(yrange), xlabel=&quot;x₁&quot;, ylabel=&quot;x₂&quot;, legend=false)</code></pre><img src="7c351ee5.svg" alt="Example block output"/><p>While the draws do a poor job of covering the tails of the distribution, they are still useful for identifying the nonlinear correlation between these two parameters.</p><h2 id="A-100-dimensional-funnel"><a class="docs-heading-anchor" href="#A-100-dimensional-funnel">A 100-dimensional funnel</a><a id="A-100-dimensional-funnel-1"></a><a class="docs-heading-anchor-permalink" href="#A-100-dimensional-funnel" title="Permalink"></a></h2><p>As we have seen above, running multi-path Pathfinder is much more useful for target distributions that are far from normal. One particularly difficult distribution to sample is Neal&#39;s funnel:</p><p class="math-container">\[\begin{aligned}
plot!(xlims=extrema(xrange), ylims=extrema(yrange), xlabel=&quot;x₁&quot;, ylabel=&quot;x₂&quot;, legend=false)</code></pre><img src="413fa5d2.svg" alt="Example block output"/><p>While the draws do a poor job of covering the tails of the distribution, they are still useful for identifying the nonlinear correlation between these two parameters.</p><h2 id="A-100-dimensional-funnel"><a class="docs-heading-anchor" href="#A-100-dimensional-funnel">A 100-dimensional funnel</a><a id="A-100-dimensional-funnel-1"></a><a class="docs-heading-anchor-permalink" href="#A-100-dimensional-funnel" title="Permalink"></a></h2><p>As we have seen above, running multi-path Pathfinder is much more useful for target distributions that are far from normal. One particularly difficult distribution to sample is Neal&#39;s funnel:</p><p class="math-container">\[\begin{aligned}
\tau &amp;\sim \mathrm{Normal}(\mu=0, \sigma=3)\\
\beta_i &amp;\sim \mathrm{Normal}(\mu=0, \sigma=e^{\tau/2})
\end{aligned}\]</p><p>Such funnel geometries appear in other models (e.g. many hierarchical models) and typically frustrate MCMC sampling. Multi-path Pathfinder can&#39;t sample the funnel well, but it can quickly give us draws that can help us diagnose that we have a funnel.</p><p>In this example, we draw from a 100-dimensional funnel and visualize 2 dimensions.</p><pre><code class="language-julia hljs">using ReverseDiff, ADTypes
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contour(τ_range, β₁_range, exp ∘ logp_funnel ∘ Base.vect)
scatter!(τ_approx, β₁_approx; msw=0, ms=2, alpha=0.5, color=1)
plot!(; xlims=extrema(τ_range), ylims=extrema(β₁_range), xlabel=&quot;τ&quot;, ylabel=&quot;β₁&quot;, legend=false)</code></pre><img src="ae89033d.svg" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../lib/internals/">« Internals</a><a class="docs-footer-nextpage" href="../initializing-hmc/">Initializing HMC »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 24 November 2024 00:24">Sunday 24 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
plot!(; xlims=extrema(τ_range), ylims=extrema(β₁_range), xlabel=&quot;τ&quot;, ylabel=&quot;β₁&quot;, legend=false)</code></pre><img src="19b18f23.svg" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../lib/internals/">« Internals</a><a class="docs-footer-nextpage" href="../initializing-hmc/">Initializing HMC »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Monday 25 November 2024 00:23">Monday 25 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
10 changes: 5 additions & 5 deletions dev/examples/turing/index.html
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Iterations = 501:1:1500
Number of chains = 8
Samples per chain = 1000
Wall duration = 6.8 seconds
Compute duration = 5.09 seconds
Wall duration = 6.75 seconds
Compute duration = 4.94 seconds
parameters = α, β, σ
internals = lp, n_steps, is_accept, acceptance_rate, log_density, hamiltonian_energy, hamiltonian_energy_error, max_hamiltonian_energy_error, tree_depth, numerical_error, step_size, nom_step_size

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Iterations = 51:1:1050
Number of chains = 8
Samples per chain = 1000
Wall duration = 2.72 seconds
Compute duration = 2.32 seconds
Wall duration = 2.87 seconds
Compute duration = 2.46 seconds
parameters = α, β, σ
internals = lp, n_steps, is_accept, acceptance_rate, log_density, hamiltonian_energy, hamiltonian_energy_error, max_hamiltonian_energy_error, tree_depth, numerical_error, step_size, nom_step_size, is_adapt

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α 1.3916 1.4468 1.4750 1.5028 1.5585
β 1.9914 2.0011 2.0061 2.0110 2.0205
σ 0.1890 0.2057 0.2160 0.2267 0.2501
</code></pre><p>See <a href="../initializing-hmc/#Initializing-HMC-with-Pathfinder">Initializing HMC with Pathfinder</a> for further examples.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../initializing-hmc/">« Initializing HMC</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 24 November 2024 00:24">Sunday 24 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
</code></pre><p>See <a href="../initializing-hmc/#Initializing-HMC-with-Pathfinder">Initializing HMC with Pathfinder</a> for further examples.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../initializing-hmc/">« Initializing HMC</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Monday 25 November 2024 00:23">Monday 25 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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