build based on 4722d43

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.7.3","generation_timestamp":"2023-10-13T07:55:05","documenter_version":"1.1.1"}}
+{"documenter":{"julia_version":"1.7.3","generation_timestamp":"2023-11-04T00:53:50","documenter_version":"1.1.2"}}

dev/framework/index.html

@@ -4,4 +4,4 @@
 \equiv
 \underset{\boldsymbol{\gamma}}{\mathrm{arg\,min}} \; r_{\Omega}(\hat{\boldsymbol{\theta}}(\cdot; \boldsymbol{\gamma})).\]</p><p>Typically, <span>$r_{\Omega}(\cdot)$</span> cannot be directly evaluated, but it can be approximated using Monte Carlo methods. Specifically, given a set of <span>$K$</span> parameter vectors sampled from the prior <span>$\Omega(\cdot)$</span> denoted by <span>$\vartheta$</span> and, for each <span>$\boldsymbol{\theta} \in \vartheta$</span>, <span>$J$</span> realisations from <span>$f(\boldsymbol{z} \mid  \boldsymbol{\theta})$</span> collected in <span>$\mathcal{Z}_{\boldsymbol{\theta}}$</span>,</p><p class="math-container">\[ r_{\Omega}(\hat{\boldsymbol{\theta}}(\cdot; \boldsymbol{\gamma}))
  \approx
-\frac{1}{K} \sum_{\boldsymbol{\theta} \in \vartheta} \frac{1}{J} \sum_{\boldsymbol{z} \in \mathcal{Z}_{\boldsymbol{\theta}}} L(\boldsymbol{\theta}, \hat{\boldsymbol{\theta}}(\boldsymbol{z}; \boldsymbol{\gamma})).  \]</p><p>Note that the above approximation does not involve evaluation, or knowledge, of the likelihood function.</p><p>The Monte-Carlo-approximated Bayes risk can be straightforwardly minimised with respect to <span>$\boldsymbol{\gamma}$</span> using back-propagation and stochastic gradient descent. For sufficiently flexible architectures, the point estimator targets a Bayes estimator with respect to <span>$L(\cdot, \cdot)$</span> and <span>$\Omega(\cdot)$</span>. We therefore call the fitted neural point estimator a  <em>neural Bayes estimator</em>. Like Bayes estimators, neural Bayes estimators target a specific point summary of the posterior distribution. For instance, the absolute-error and squared-error loss functions lead to neural Bayes estimators that approximate the posterior median and mean, respectively.</p><h3 id="Construction-of-neural-Bayes-estimators"><a class="docs-heading-anchor" href="#Construction-of-neural-Bayes-estimators">Construction of neural Bayes estimators</a><a id="Construction-of-neural-Bayes-estimators-1"></a><a class="docs-heading-anchor-permalink" href="#Construction-of-neural-Bayes-estimators" title="Permalink"></a></h3><p>The neural Bayes estimators is conceptually simple and can be used in a wide range of problems where other approaches, such as maximum-likelihood estimation, are computationally infeasible. The estimator also has marked practical appeal, as the general workflow for its construction is only loosely connected to the statistical or physical model being considered. The workflow is as follows:</p><ol><li>Define the prior, <span>$\Omega(\cdot)$</span>.</li><li>Choose a loss function, <span>$L(\cdot, \cdot)$</span>, typically the absolute-error or squared-error loss.</li><li>Design a suitable neural-network architecture for the neural point estimator <span>$\hat{\boldsymbol{\theta}}(\cdot; \boldsymbol{\gamma})$</span>.</li><li>Sample parameters from <span>$\Omega(\cdot)$</span> to form training/validation/test parameter sets.</li><li>Given the above parameter sets, simulate data from the model, to form training/validation/test data sets.</li><li>Train the neural network (i.e., estimate <span>$\boldsymbol{\gamma}$</span>) by minimising the loss function averaged over the training sets. During training, monitor performance and convergence using the validation sets.</li><li>Assess the fitted neural Bayes estimator, <span>$\hat{\boldsymbol{\theta}}(\cdot; \boldsymbol{\gamma}^*)$</span>, using the test set.</li></ol></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« NeuralEstimators</a><a class="docs-footer-nextpage" href="../workflow/overview/">Overview »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.1 on <span class="colophon-date" title="Friday 13 October 2023 07:55">Friday 13 October 2023</span>. Using Julia version 1.7.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+\frac{1}{K} \sum_{\boldsymbol{\theta} \in \vartheta} \frac{1}{J} \sum_{\boldsymbol{z} \in \mathcal{Z}_{\boldsymbol{\theta}}} L(\boldsymbol{\theta}, \hat{\boldsymbol{\theta}}(\boldsymbol{z}; \boldsymbol{\gamma})).  \]</p><p>Note that the above approximation does not involve evaluation, or knowledge, of the likelihood function.</p><p>The Monte-Carlo-approximated Bayes risk can be straightforwardly minimised with respect to <span>$\boldsymbol{\gamma}$</span> using back-propagation and stochastic gradient descent. For sufficiently flexible architectures, the point estimator targets a Bayes estimator with respect to <span>$L(\cdot, \cdot)$</span> and <span>$\Omega(\cdot)$</span>. We therefore call the fitted neural point estimator a  <em>neural Bayes estimator</em>. Like Bayes estimators, neural Bayes estimators target a specific point summary of the posterior distribution. For instance, the absolute-error and squared-error loss functions lead to neural Bayes estimators that approximate the posterior median and mean, respectively.</p><h3 id="Construction-of-neural-Bayes-estimators"><a class="docs-heading-anchor" href="#Construction-of-neural-Bayes-estimators">Construction of neural Bayes estimators</a><a id="Construction-of-neural-Bayes-estimators-1"></a><a class="docs-heading-anchor-permalink" href="#Construction-of-neural-Bayes-estimators" title="Permalink"></a></h3><p>The neural Bayes estimators is conceptually simple and can be used in a wide range of problems where other approaches, such as maximum-likelihood estimation, are computationally infeasible. The estimator also has marked practical appeal, as the general workflow for its construction is only loosely connected to the statistical or physical model being considered. The workflow is as follows:</p><ol><li>Define the prior, <span>$\Omega(\cdot)$</span>.</li><li>Choose a loss function, <span>$L(\cdot, \cdot)$</span>, typically the absolute-error or squared-error loss.</li><li>Design a suitable neural-network architecture for the neural point estimator <span>$\hat{\boldsymbol{\theta}}(\cdot; \boldsymbol{\gamma})$</span>.</li><li>Sample parameters from <span>$\Omega(\cdot)$</span> to form training/validation/test parameter sets.</li><li>Given the above parameter sets, simulate data from the model, to form training/validation/test data sets.</li><li>Train the neural network (i.e., estimate <span>$\boldsymbol{\gamma}$</span>) by minimising the loss function averaged over the training sets. During training, monitor performance and convergence using the validation sets.</li><li>Assess the fitted neural Bayes estimator, <span>$\hat{\boldsymbol{\theta}}(\cdot; \boldsymbol{\gamma}^*)$</span>, using the test set.</li></ol></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« NeuralEstimators</a><a class="docs-footer-nextpage" href="../workflow/overview/">Overview »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Saturday 4 November 2023 00:53">Saturday 4 November 2023</span>. Using Julia version 1.7.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/index.html

@@ -7,4 +7,4 @@
 	volume = {to appear},
 	doi = {10.1080/00031305.2023.2249522},
 	url = {https://doi.org/10.1080/00031305.2023.2249522}
-}</code></pre></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="framework/">Theoretical framework »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.1 on <span class="colophon-date" title="Friday 13 October 2023 07:55">Friday 13 October 2023</span>. Using Julia version 1.7.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+}</code></pre></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="framework/">Theoretical framework »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Saturday 4 November 2023 00:53">Saturday 4 November 2023</span>. Using Julia version 1.7.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/workflow/advancedusage/index.html

@@ -24,4 +24,4 @@
 end</code></pre><p>Then, setting the argument <code>m</code> in <a href="../../API/core/#NeuralEstimators.train"><code>train</code></a> to be an integer range (e.g., <code>1:30</code>) will train the neural estimator with the given variable sample sizes.</p><h2 id="Combining-neural-and-expert-summary-statistics"><a class="docs-heading-anchor" href="#Combining-neural-and-expert-summary-statistics">Combining neural and expert summary statistics</a><a id="Combining-neural-and-expert-summary-statistics-1"></a><a class="docs-heading-anchor-permalink" href="#Combining-neural-and-expert-summary-statistics" title="Permalink"></a></h2><p>See <a href="../../API/architectures/#NeuralEstimators.DeepSetExpert"><code>DeepSetExpert</code></a>.</p><h2 id="Loading-previously-saved-neural-estimators"><a class="docs-heading-anchor" href="#Loading-previously-saved-neural-estimators">Loading previously saved neural estimators</a><a id="Loading-previously-saved-neural-estimators-1"></a><a class="docs-heading-anchor-permalink" href="#Loading-previously-saved-neural-estimators" title="Permalink"></a></h2><p>As training is by far the most computationally demanding part of the workflow, one typically trains an estimator and then saves it for later use. More specifically, one usually saves the <em>parameters</em> of the neural estimator (e.g., the weights and biases of the neural networks); then, to load the neural estimator at a later time, one initialises an estimator with the same architecture used during training, and then loads the saved parameters into this estimator.</p><p>If the argument <code>savepath</code> is specified, <a href="../../API/core/#NeuralEstimators.train"><code>train</code></a> automatically saves the neural estimator&#39;s parameters; to load them, one may use the following code, or similar:</p><pre><code class="nohighlight hljs">using Flux: loadparams!
 
 θ̂ = architecture()
-loadparams!(θ̂, loadbestweights(savepath))</code></pre><p>Above, <code>architecture()</code> is a user-defined function that returns a neural estimator with the same architecture as the estimator that we wish to load, but with randomly initialised parameters, and the function <code>loadparams!</code> loads the parameters of the best (as determined by <a href="../../API/utility/#NeuralEstimators.loadbestweights"><code>loadbestweights</code></a>) neural estimator saved in <code>savepath</code>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../examples/">« Examples</a><a class="docs-footer-nextpage" href="../../API/core/">Core »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.1 on <span class="colophon-date" title="Friday 13 October 2023 07:55">Friday 13 October 2023</span>. Using Julia version 1.7.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+loadparams!(θ̂, loadbestweights(savepath))</code></pre><p>Above, <code>architecture()</code> is a user-defined function that returns a neural estimator with the same architecture as the estimator that we wish to load, but with randomly initialised parameters, and the function <code>loadparams!</code> loads the parameters of the best (as determined by <a href="../../API/utility/#NeuralEstimators.loadbestweights"><code>loadbestweights</code></a>) neural estimator saved in <code>savepath</code>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../examples/">« Examples</a><a class="docs-footer-nextpage" href="../../API/core/">Core »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Saturday 4 November 2023 00:53">Saturday 4 November 2023</span>. Using Julia version 1.7.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/workflow/examples/index.html

@@ -137,4 +137,4 @@
 
 # Parametric bootstrap sample and bootstrap confidence interval
 θ̃ = bootstrap(θ̂, Parameters(θ̂(z), S), simulate, 1)   
-interval(θ̃)  					                </code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../overview/">« Overview</a><a class="docs-footer-nextpage" href="../advancedusage/">Advanced usage »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.1 on <span class="colophon-date" title="Friday 13 October 2023 07:55">Friday 13 October 2023</span>. Using Julia version 1.7.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+interval(θ̃)  					                </code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../overview/">« Overview</a><a class="docs-footer-nextpage" href="../advancedusage/">Advanced usage »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Saturday 4 November 2023 00:53">Saturday 4 November 2023</span>. Using Julia version 1.7.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>