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\end{aligned}$$</code></pre><ol><li>When using equations, make sure not to follow the left-hand <code>$$</code> or <code>$</code> with a space, but instead directly start the equation, e.g. not <code>$$ a + b $$</code>, but <code>$$a + b$$</code>. For equations that are supposed to be on a separate line, make sure <code>$$...$$</code> is preceded and followed by an empty line.</li><li>Notebooks and plain Julia have different scoping rules for global variables. It may happen that the generation of your example fails due to an <code>UndefVarError</code> or other scoping issues. In these cases we recommend using <code>let ... end</code> blocks to enforce local scoping or use the <code>global</code> keyword to disambiguate the scoping rules, e.g.</li></ol><pre><code class="language-julia hljs">variable = 0
for i in 1:10
global variable = variable + i
end</code></pre><ol><li>All examples must use and activate the local environment specified by <code>Project.toml</code> in the second cell (see <code>1.</code>). Please have a look at the existing notebooks for an example on how to activate this local environment. If you need additional packages, you can add then to the <code>(examples)</code> project.</li><li>All plots should be displayed automatically. In special cases, if needed, save figures in the <code>../pics/figure-name.ext</code> format. Might be useful for saving gifs. Use <code>![](../pics/figure-name.ext)</code> to display a static image.</li></ol><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Please avoid adding <code>PyPlot</code> in the <code>(examples)</code> project. Installing and building <code>PyPlot</code> dependencies takes several minutes on every CI run. Use <code>Plots</code> instead.</p></div></div><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Use <code>make examples</code> to run all examples or <code>make examples specific=MyNewCoolNotebook</code> to run any notebook that includes <code>MyNewCoolNotebook</code> in its file name.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../overview/">« Overview</a><a class="docs-footer-nextpage" href="../new-release/">Publishing a new release »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 28 August 2023 08:18">Monday 28 August 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
end</code></pre><ol><li>All examples must use and activate the local environment specified by <code>Project.toml</code> in the second cell (see <code>1.</code>). Please have a look at the existing notebooks for an example on how to activate this local environment. If you need additional packages, you can add then to the <code>(examples)</code> project.</li><li>All plots should be displayed automatically. In special cases, if needed, save figures in the <code>../pics/figure-name.ext</code> format. Might be useful for saving gifs. Use <code>![](../pics/figure-name.ext)</code> to display a static image.</li></ol><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Please avoid adding <code>PyPlot</code> in the <code>(examples)</code> project. Installing and building <code>PyPlot</code> dependencies takes several minutes on every CI run. Use <code>Plots</code> instead.</p></div></div><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Use <code>make examples</code> to run all examples or <code>make examples specific=MyNewCoolNotebook</code> to run any notebook that includes <code>MyNewCoolNotebook</code> in its file name.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../overview/">« Overview</a><a class="docs-footer-nextpage" href="../new-release/">Publishing a new release »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 28 August 2023 08:54">Monday 28 August 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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end

# The animation is saved and displayed as markdown picture for the automatic HTML generation
gif(animation_ai, &quot;../pics/ai-mountain-car-ai.gif&quot;, fps = 24, show_msg = false);</code></pre><p><img src="../../../assets/examples/pics/ai-mountain-car-ai.gif" alt/></p><p>Voila! The car now is able to reach the camping site with a smart strategy.</p><p>The left figure shows the agent reached its goal by swinging and the right one shows the corresponding engine force. As we can see, at the beginning the agent tried to reach the goal directly (with full engine force) but after some trials it realized that&#39;s not possible. Since the agent looks ahead for 50 time steps, it has enough time to explore other policies, helping it learn to move back to get more momentum to reach the goal.</p><p>Now our friends can enjoy their trip at the camping site!. </p><h1 id="Reference"><a class="docs-heading-anchor" href="#Reference">Reference</a><a id="Reference-1"></a><a class="docs-heading-anchor-permalink" href="#Reference" title="Permalink"></a></h1><p>We refer reader to the Thijs van de Laar (2019) &quot;Simulating active inference processes by message passing&quot; original paper with more in-depth overview and explanation of the active inference agent implementation by message passing. The original environment/task description is from Ueltzhoeffer (2017) &quot;Deep active inference&quot;.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../overview/">« Overview</a><a class="docs-footer-nextpage" href="../Advanced Tutorial/">Advanced Tutorial »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 28 August 2023 08:18">Monday 28 August 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
gif(animation_ai, &quot;../pics/ai-mountain-car-ai.gif&quot;, fps = 24, show_msg = false);</code></pre><p><img src="../../../assets/examples/pics/ai-mountain-car-ai.gif" alt/></p><p>Voila! The car now is able to reach the camping site with a smart strategy.</p><p>The left figure shows the agent reached its goal by swinging and the right one shows the corresponding engine force. As we can see, at the beginning the agent tried to reach the goal directly (with full engine force) but after some trials it realized that&#39;s not possible. Since the agent looks ahead for 50 time steps, it has enough time to explore other policies, helping it learn to move back to get more momentum to reach the goal.</p><p>Now our friends can enjoy their trip at the camping site!. </p><h1 id="Reference"><a class="docs-heading-anchor" href="#Reference">Reference</a><a id="Reference-1"></a><a class="docs-heading-anchor-permalink" href="#Reference" title="Permalink"></a></h1><p>We refer reader to the Thijs van de Laar (2019) &quot;Simulating active inference processes by message passing&quot; original paper with more in-depth overview and explanation of the active inference agent implementation by message passing. The original environment/task description is from Ueltzhoeffer (2017) &quot;Deep active inference&quot;.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../overview/">« Overview</a><a class="docs-footer-nextpage" href="../Advanced Tutorial/">Advanced Tutorial »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 28 August 2023 08:54">Monday 28 August 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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[y[4]][Bernoulli][p]: VariationalMessage()
[y[5]][Bernoulli][p]: VariationalMessage()
New posterior marginal for θ: Marginal(Beta{Float64}(α=4.0, β=10.0))</code></pre><pre><code class="language-julia hljs">unsubscribe!(θ_subscription)</code></pre><pre><code class="language-julia hljs"># Inference is lazy and does not send messages if no one is listening for them
update!(y, coinflips)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Active Inference Mountain car/">« Active Inference Mountain car</a><a class="docs-footer-nextpage" href="../Assessing People Skills/">Assessing People’s Skills »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 28 August 2023 08:18">Monday 28 August 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
update!(y, coinflips)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Active Inference Mountain car/">« Active Inference Mountain car</a><a class="docs-footer-nextpage" href="../Assessing People Skills/">Assessing People’s Skills »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 28 August 2023 08:54">Monday 28 August 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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map(params, inference_result.posteriors[:s])</code></pre><pre><code class="nohighlight hljs">3-element Vector{Tuple{Float64}}:
(0.9872448979591837,)
(0.06377551020408162,)
(0.4719387755102041,)</code></pre><p>These results suggest that this particular student was very likely out on the town last night.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Advanced Tutorial/">« Advanced Tutorial</a><a class="docs-footer-nextpage" href="../Chance Constraints/">Chance-Constrained Active Inference »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 28 August 2023 08:18">Monday 28 August 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
(0.4719387755102041,)</code></pre><p>These results suggest that this particular student was very likely out on the town last night.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Advanced Tutorial/">« Advanced Tutorial</a><a class="docs-footer-nextpage" href="../Chance Constraints/">Chance-Constrained Active Inference »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 28 August 2023 08:54">Monday 28 August 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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