build based on a0f0c2c

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-08-31T07:32:40","documenter_version":"1.6.0"}}
+{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-08-31T08:43:44","documenter_version":"1.6.0"}}

dev/exponential/index.html

@@ -97,4 +97,4 @@
     axis_kwargs=(width=600, height=300))
 resize_to_layout!(fig)</code></pre><figure>
     <img src='../figures/linear_exponential_example.png', alt'Linear exponential profiles'><br>
-</figure></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../logistic/">« Example II: Logistic ordinary differential equation</a><a class="docs-footer-nextpage" href="../lotka/">Example IV: Lotka-Volterra ODE and computing bivarate profile likelihoods »</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 1.6.0 on <span class="colophon-date" title="Saturday 31 August 2024 07:32">Saturday 31 August 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</figure></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../logistic/">« Example II: Logistic ordinary differential equation</a><a class="docs-footer-nextpage" href="../lotka/">Example IV: Lotka-Volterra ODE and computing bivarate profile likelihoods »</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 1.6.0 on <span class="colophon-date" title="Saturday 31 August 2024 08:43">Saturday 31 August 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/heat/index.html

@@ -479,4 +479,4 @@
 q_lwr = minimum(q_mat; dims=2) |> vec
 q_upr = maximum(q_mat; dims=2) |> vec
 lines!(ax, t_many_pts, q_lwr, color=:magenta)
-lines!(ax, t_many_pts, q_upr, color=:magenta)</code></pre></article><nav class="docs-footer"><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 1.6.0 on <span class="colophon-date" title="Saturday 31 August 2024 07:32">Saturday 31 August 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+lines!(ax, t_many_pts, q_upr, color=:magenta)</code></pre></article><nav class="docs-footer"><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 1.6.0 on <span class="colophon-date" title="Saturday 31 August 2024 08:43">Saturday 31 August 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/interface/index.html

@@ -27,4 +27,4 @@
     interpolants::Dict{I,Spl}
     confidence_regions::Dict{I,ConfidenceRegion{CT,CF}}
     other_mles::OM
-end</code></pre><p>The definitions are similar to the univariate case, although <code>parameter_values</code> now maps to <code>Tuple</code>s of grids, making use of <code>OffsetVector</code>s to define grids relative to an MLE. Similarly, we use <code>OffsetMatrix</code>s to define the grid of profile values, given in <code>profile_values</code>. You can also call the resulting struct, e.g. if <code>prof</code> is a <code>BivariateProfileLikelihoodSolution</code>, then <code>prof(0.3, 0.9, :λ, :K)</code> computes the bivariate profile between <span>$\lambda$</span> and <span>$K$</span> at <span>$(\lambda,K)=(0.3,0.9)$</span>. See <code>?ProfileLikelihood.BivariateProfileLikelihoodSolution</code> for more detail, or its docstring in the sidebar. </p><p>You can also index such a <code>prof</code> to look at only a specific parameter. For example, <code>prof[1, 2]</code> will return a <code>BivariateProfileLikelihoodSolutionView</code> for the profile between the first and second parameter. Similarly, <code>prof[:λ, :K]</code> is the profile between <span>$\lambda$</span> and <span>$K$</span>.</p><h2 id="Propagating-uncertainty:-Prediction-intervals"><a class="docs-heading-anchor" href="#Propagating-uncertainty:-Prediction-intervals">Propagating uncertainty: Prediction intervals</a><a id="Propagating-uncertainty:-Prediction-intervals-1"></a><a class="docs-heading-anchor-permalink" href="#Propagating-uncertainty:-Prediction-intervals" title="Permalink"></a></h2><p>The confidence intervals obtained from profiling can be used to obtain approximate prediction intervals via <em>profile-wise profile likelihoods</em>, as defined e.g. in <a href="https://doi.org/10.1101/2022.12.14.520367">Simpson and Maclaren (2022)</a>, for a prediction function <span>$\boldsymbol q(\boldsymbol\theta)$</span>. These intervals can be based on varying a single parameter, or by taking the union of individual prediction intervals. The main function for this is <code>get_prediction_intervals</code>. Rather than explain in full detail here, please refer to the second example (the logistic ODE example), where we reproduce the first case study of <a href="https://doi.org/10.1101/2022.12.14.520367">Simpson and Maclaren (2022)</a>.</p><p>The full docstring for <code>get_prediction_intervals</code> is given in the sidebar.</p><h2 id="Plotting"><a class="docs-heading-anchor" href="#Plotting">Plotting</a><a id="Plotting-1"></a><a class="docs-heading-anchor-permalink" href="#Plotting" title="Permalink"></a></h2><p>We provide a function <code>plot_profiles</code> that can be useful for plotting profile likelihoods. It requires that you have done </p><pre><code class="language-julia hljs">using CairoMakie # (or any other Makie backend)</code></pre><p>(else the function does not exist, thanks to Requires.jl and package extensions from Julia v1.9). A full description of this function is given in the corresponding docstring in the sidebar.</p><h2 id="GridSearch"><a class="docs-heading-anchor" href="#GridSearch">GridSearch</a><a id="GridSearch-1"></a><a class="docs-heading-anchor-permalink" href="#GridSearch" title="Permalink"></a></h2><p>it can sometimes be useful to evaluate the likelihood function over many points prior to optimising it, e.g. to find a good initial estimate or to just obtain data at many points for the purpose of visualisation. We provide functions for this, based on either a <code>RegularGrid</code> or an <code>IrregularGrid</code>.</p><p>A <code>RegularGrid</code> is a grid in which the grid for each parameter is uniformly spaced, so that the values for all parameter values to try fall on a lattice. An <code>IrregularGrid</code> allows for the parameters to take on whatever values you want, with the requirement that the parameter values to evaluate at are provided as a matrix with each column a different parameter set.</p><p>The function <code>grid_search</code>, after having defined a grid, can then be used for performing the grid search. The main method of interest is:</p><pre><code class="language-julia hljs">grid_search(prob::LikelihoodProblem, grid::AbstractGrid; save_vals=Val(false), parallel=Val(false))</code></pre><p>Here, <code>grid</code> could be either a <code>RegularGrid</code> or an <code>IrregularGrid</code>. You can set <code>save_vals=Val(true)</code> if you want an array with all the likelihood function values, <code>Val(false)</code> otherwise. To enable multithreading, allowing for the evaluation of the function across different points via multiple threads, set <code>parallel=Val(true)</code>, otherwise leave it as <code>Val(false)</code>. The result of this grid search, if <code>save_vals=Val(true)</code>, will be <code>(sol, f_vals)</code>, where <code>sol</code> is a likelihood solution giving the parameters that gave to the highest likelihood, and <code>f_res</code> is the array of likelihoods at the corresponding parameters. If <code>save_vals=Val(false)</code>, only <code>sol</code> is returned.</p><p>More detail is given in the examples, and complete docstrings are provided in the sidebar.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../docstrings/">Docstrings »</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 1.6.0 on <span class="colophon-date" title="Saturday 31 August 2024 07:32">Saturday 31 August 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end</code></pre><p>The definitions are similar to the univariate case, although <code>parameter_values</code> now maps to <code>Tuple</code>s of grids, making use of <code>OffsetVector</code>s to define grids relative to an MLE. Similarly, we use <code>OffsetMatrix</code>s to define the grid of profile values, given in <code>profile_values</code>. You can also call the resulting struct, e.g. if <code>prof</code> is a <code>BivariateProfileLikelihoodSolution</code>, then <code>prof(0.3, 0.9, :λ, :K)</code> computes the bivariate profile between <span>$\lambda$</span> and <span>$K$</span> at <span>$(\lambda,K)=(0.3,0.9)$</span>. See <code>?ProfileLikelihood.BivariateProfileLikelihoodSolution</code> for more detail, or its docstring in the sidebar. </p><p>You can also index such a <code>prof</code> to look at only a specific parameter. For example, <code>prof[1, 2]</code> will return a <code>BivariateProfileLikelihoodSolutionView</code> for the profile between the first and second parameter. Similarly, <code>prof[:λ, :K]</code> is the profile between <span>$\lambda$</span> and <span>$K$</span>.</p><h2 id="Propagating-uncertainty:-Prediction-intervals"><a class="docs-heading-anchor" href="#Propagating-uncertainty:-Prediction-intervals">Propagating uncertainty: Prediction intervals</a><a id="Propagating-uncertainty:-Prediction-intervals-1"></a><a class="docs-heading-anchor-permalink" href="#Propagating-uncertainty:-Prediction-intervals" title="Permalink"></a></h2><p>The confidence intervals obtained from profiling can be used to obtain approximate prediction intervals via <em>profile-wise profile likelihoods</em>, as defined e.g. in <a href="https://doi.org/10.1101/2022.12.14.520367">Simpson and Maclaren (2022)</a>, for a prediction function <span>$\boldsymbol q(\boldsymbol\theta)$</span>. These intervals can be based on varying a single parameter, or by taking the union of individual prediction intervals. The main function for this is <code>get_prediction_intervals</code>. Rather than explain in full detail here, please refer to the second example (the logistic ODE example), where we reproduce the first case study of <a href="https://doi.org/10.1101/2022.12.14.520367">Simpson and Maclaren (2022)</a>.</p><p>The full docstring for <code>get_prediction_intervals</code> is given in the sidebar.</p><h2 id="Plotting"><a class="docs-heading-anchor" href="#Plotting">Plotting</a><a id="Plotting-1"></a><a class="docs-heading-anchor-permalink" href="#Plotting" title="Permalink"></a></h2><p>We provide a function <code>plot_profiles</code> that can be useful for plotting profile likelihoods. It requires that you have done </p><pre><code class="language-julia hljs">using CairoMakie # (or any other Makie backend)</code></pre><p>(else the function does not exist, thanks to Requires.jl and package extensions from Julia v1.9). A full description of this function is given in the corresponding docstring in the sidebar.</p><h2 id="GridSearch"><a class="docs-heading-anchor" href="#GridSearch">GridSearch</a><a id="GridSearch-1"></a><a class="docs-heading-anchor-permalink" href="#GridSearch" title="Permalink"></a></h2><p>it can sometimes be useful to evaluate the likelihood function over many points prior to optimising it, e.g. to find a good initial estimate or to just obtain data at many points for the purpose of visualisation. We provide functions for this, based on either a <code>RegularGrid</code> or an <code>IrregularGrid</code>.</p><p>A <code>RegularGrid</code> is a grid in which the grid for each parameter is uniformly spaced, so that the values for all parameter values to try fall on a lattice. An <code>IrregularGrid</code> allows for the parameters to take on whatever values you want, with the requirement that the parameter values to evaluate at are provided as a matrix with each column a different parameter set.</p><p>The function <code>grid_search</code>, after having defined a grid, can then be used for performing the grid search. The main method of interest is:</p><pre><code class="language-julia hljs">grid_search(prob::LikelihoodProblem, grid::AbstractGrid; save_vals=Val(false), parallel=Val(false))</code></pre><p>Here, <code>grid</code> could be either a <code>RegularGrid</code> or an <code>IrregularGrid</code>. You can set <code>save_vals=Val(true)</code> if you want an array with all the likelihood function values, <code>Val(false)</code> otherwise. To enable multithreading, allowing for the evaluation of the function across different points via multiple threads, set <code>parallel=Val(true)</code>, otherwise leave it as <code>Val(false)</code>. The result of this grid search, if <code>save_vals=Val(true)</code>, will be <code>(sol, f_vals)</code>, where <code>sol</code> is a likelihood solution giving the parameters that gave to the highest likelihood, and <code>f_res</code> is the array of likelihoods at the corresponding parameters. If <code>save_vals=Val(false)</code>, only <code>sol</code> is returned.</p><p>More detail is given in the examples, and complete docstrings are provided in the sidebar.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../docstrings/">Docstrings »</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 1.6.0 on <span class="colophon-date" title="Saturday 31 August 2024 08:43">Saturday 31 August 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>