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<!DOCTYPE html>
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<ul class="summary">
<img src="./nimble-icon.png"
width=100>
<li><a href="./cha-welcome-nimble.html">NIMBLE User Manual, Version 1.4.2</a></li>
<li><a href="https://github.com/nimble-dev/nimble">NIMBLE Development Team</a></li>
<li><a href="https://R-nimble.org">https://R-nimble.org</a></li>
<li class="divider"></li>
<li class="part"><span><b>I Introduction</b></span></li>
<li class="chapter" data-level="1" data-path="cha-welcome-nimble.html"><a href="cha-welcome-nimble.html"><i class="fa fa-check"></i><b>1</b> Welcome to NIMBLE</a>
<ul>
<li class="chapter" data-level="1.1" data-path="cha-welcome-nimble.html"><a href="cha-welcome-nimble.html#sec:what-is-nimble"><i class="fa fa-check"></i><b>1.1</b> What does NIMBLE do?</a></li>
<li class="chapter" data-level="1.2" data-path="cha-welcome-nimble.html"><a href="cha-welcome-nimble.html#how-to-use-this-manual"><i class="fa fa-check"></i><b>1.2</b> How to use this manual</a></li>
</ul></li>
<li class="chapter" data-level="2" data-path="cha-lightning-intro.html"><a href="cha-lightning-intro.html"><i class="fa fa-check"></i><b>2</b> Lightning introduction</a>
<ul>
<li class="chapter" data-level="2.1" data-path="cha-lightning-intro.html"><a href="cha-lightning-intro.html#sec:brief-example"><i class="fa fa-check"></i><b>2.1</b> A brief example</a></li>
<li class="chapter" data-level="2.2" data-path="cha-lightning-intro.html"><a href="cha-lightning-intro.html#sec:creating-model"><i class="fa fa-check"></i><b>2.2</b> Creating a model</a></li>
<li class="chapter" data-level="2.3" data-path="cha-lightning-intro.html"><a href="cha-lightning-intro.html#sec:compiling-model"><i class="fa fa-check"></i><b>2.3</b> Compiling the model</a></li>
<li class="chapter" data-level="2.4" data-path="cha-lightning-intro.html"><a href="cha-lightning-intro.html#sec:intro-runMCMC"><i class="fa fa-check"></i><b>2.4</b> One-line invocation of MCMC</a></li>
<li class="chapter" data-level="2.5" data-path="cha-lightning-intro.html"><a href="cha-lightning-intro.html#sec:creating-mcmc"><i class="fa fa-check"></i><b>2.5</b> Creating, compiling and running a basic MCMC configuration</a></li>
<li class="chapter" data-level="2.6" data-path="cha-lightning-intro.html"><a href="cha-lightning-intro.html#sec:customizing-mcmc"><i class="fa fa-check"></i><b>2.6</b> Customizing the MCMC</a></li>
<li class="chapter" data-level="2.7" data-path="cha-lightning-intro.html"><a href="cha-lightning-intro.html#sec:running-mcem"><i class="fa fa-check"></i><b>2.7</b> Running MCEM</a></li>
<li class="chapter" data-level="2.8" data-path="cha-lightning-intro.html"><a href="cha-lightning-intro.html#sec:creating-your-own"><i class="fa fa-check"></i><b>2.8</b> Creating your own functions</a></li>
</ul></li>
<li class="chapter" data-level="3" data-path="cha-more-introduction.html"><a href="cha-more-introduction.html"><i class="fa fa-check"></i><b>3</b> More introduction</a>
<ul>
<li class="chapter" data-level="3.1" data-path="cha-more-introduction.html"><a href="cha-more-introduction.html#nimble-adopts-and-extends-the-bugs-language-for-specifying-models"><i class="fa fa-check"></i><b>3.1</b> NIMBLE adopts and extends the BUGS language for specifying models</a></li>
<li class="chapter" data-level="3.2" data-path="cha-more-introduction.html"><a href="cha-more-introduction.html#sec:nimble-lang-writ"><i class="fa fa-check"></i><b>3.2</b> nimbleFunctions for writing algorithms</a></li>
<li class="chapter" data-level="3.3" data-path="cha-more-introduction.html"><a href="cha-more-introduction.html#sec:nimble-algor-libr"><i class="fa fa-check"></i><b>3.3</b> The NIMBLE algorithm library</a></li>
</ul></li>
<li class="chapter" data-level="4" data-path="cha-installing-nimble.html"><a href="cha-installing-nimble.html"><i class="fa fa-check"></i><b>4</b> Installing NIMBLE</a>
<ul>
<li class="chapter" data-level="4.1" data-path="cha-installing-nimble.html"><a href="cha-installing-nimble.html#sec:requ-run-nimble"><i class="fa fa-check"></i><b>4.1</b> Requirements to run NIMBLE</a></li>
<li class="chapter" data-level="4.2" data-path="cha-installing-nimble.html"><a href="cha-installing-nimble.html#sec:compiler"><i class="fa fa-check"></i><b>4.2</b> Installing a C++ compiler for NIMBLE to use</a>
<ul>
<li class="chapter" data-level="4.2.1" data-path="cha-installing-nimble.html"><a href="cha-installing-nimble.html#macos"><i class="fa fa-check"></i><b>4.2.1</b> MacOS</a></li>
<li class="chapter" data-level="4.2.2" data-path="cha-installing-nimble.html"><a href="cha-installing-nimble.html#linux"><i class="fa fa-check"></i><b>4.2.2</b> Linux</a></li>
<li class="chapter" data-level="4.2.3" data-path="cha-installing-nimble.html"><a href="cha-installing-nimble.html#windows"><i class="fa fa-check"></i><b>4.2.3</b> Windows</a></li>
</ul></li>
<li class="chapter" data-level="4.3" data-path="cha-installing-nimble.html"><a href="cha-installing-nimble.html#installing-the-nimble-package"><i class="fa fa-check"></i><b>4.3</b> Installing the NIMBLE package</a></li>
<li class="chapter" data-level="4.4" data-path="cha-installing-nimble.html"><a href="cha-installing-nimble.html#troubleshooting-installation-problems"><i class="fa fa-check"></i><b>4.4</b> Troubleshooting installation problems</a></li>
<li class="chapter" data-level="4.5" data-path="cha-installing-nimble.html"><a href="cha-installing-nimble.html#customizing-your-installation"><i class="fa fa-check"></i><b>4.5</b> Customizing your installation</a>
<ul>
<li class="chapter" data-level="4.5.1" data-path="cha-installing-nimble.html"><a href="cha-installing-nimble.html#using-your-own-copy-of-eigen"><i class="fa fa-check"></i><b>4.5.1</b> Using your own copy of Eigen</a></li>
<li class="chapter" data-level="4.5.2" data-path="cha-installing-nimble.html"><a href="cha-installing-nimble.html#using-libnimble"><i class="fa fa-check"></i><b>4.5.2</b> Using libnimble</a></li>
<li class="chapter" data-level="4.5.3" data-path="cha-installing-nimble.html"><a href="cha-installing-nimble.html#sec:blas"><i class="fa fa-check"></i><b>4.5.3</b> BLAS and LAPACK</a></li>
<li class="chapter" data-level="4.5.4" data-path="cha-installing-nimble.html"><a href="cha-installing-nimble.html#customizing-compilation-of-the-nimble-generated-c"><i class="fa fa-check"></i><b>4.5.4</b> Customizing compilation of the NIMBLE-generated C++</a></li>
</ul></li>
</ul></li>
<li class="part"><span><b>II Models in NIMBLE</b></span></li>
<li class="chapter" data-level="5" data-path="cha-writing-models.html"><a href="cha-writing-models.html"><i class="fa fa-check"></i><b>5</b> Writing models in NIMBLE’s dialect of BUGS</a>
<ul>
<li class="chapter" data-level="5.1" data-path="cha-writing-models.html"><a href="cha-writing-models.html#sec:supp-feat-bugs"><i class="fa fa-check"></i><b>5.1</b> Comparison to BUGS dialects supported by WinBUGS, OpenBUGS and JAGS</a>
<ul>
<li class="chapter" data-level="5.1.1" data-path="cha-writing-models.html"><a href="cha-writing-models.html#supported-features-of-bugs-and-jags"><i class="fa fa-check"></i><b>5.1.1</b> Supported features of BUGS and JAGS</a></li>
<li class="chapter" data-level="5.1.2" data-path="cha-writing-models.html"><a href="cha-writing-models.html#sec:extensions-bugs"><i class="fa fa-check"></i><b>5.1.2</b> NIMBLE’s Extensions to BUGS and JAGS</a></li>
<li class="chapter" data-level="5.1.3" data-path="cha-writing-models.html"><a href="cha-writing-models.html#sec:not-yet-supported"><i class="fa fa-check"></i><b>5.1.3</b> Not-supported features of BUGS and JAGS</a></li>
</ul></li>
<li class="chapter" data-level="5.2" data-path="cha-writing-models.html"><a href="cha-writing-models.html#writing-models"><i class="fa fa-check"></i><b>5.2</b> Writing models</a>
<ul>
<li class="chapter" data-level="5.2.1" data-path="cha-writing-models.html"><a href="cha-writing-models.html#declaring-stochastic-and-deterministic-nodes"><i class="fa fa-check"></i><b>5.2.1</b> Declaring stochastic and deterministic nodes</a></li>
<li class="chapter" data-level="5.2.2" data-path="cha-writing-models.html"><a href="cha-writing-models.html#sec:more-kinds-bugs"><i class="fa fa-check"></i><b>5.2.2</b> More kinds of BUGS declarations</a></li>
<li class="chapter" data-level="5.2.3" data-path="cha-writing-models.html"><a href="cha-writing-models.html#subsec:vectorized-versus-scalar-declarations"><i class="fa fa-check"></i><b>5.2.3</b> Vectorized versus scalar declarations</a></li>
<li class="chapter" data-level="5.2.4" data-path="cha-writing-models.html"><a href="cha-writing-models.html#subsec:dists-and-functions"><i class="fa fa-check"></i><b>5.2.4</b> Available distributions</a></li>
<li class="chapter" data-level="5.2.5" data-path="cha-writing-models.html"><a href="cha-writing-models.html#subsec:BUGS-lang-fxns"><i class="fa fa-check"></i><b>5.2.5</b> Available BUGS language functions</a></li>
<li class="chapter" data-level="5.2.6" data-path="cha-writing-models.html"><a href="cha-writing-models.html#subsec:BUGS-link"><i class="fa fa-check"></i><b>5.2.6</b> Available link functions</a></li>
<li class="chapter" data-level="5.2.7" data-path="cha-writing-models.html"><a href="cha-writing-models.html#subsec:trunc"><i class="fa fa-check"></i><b>5.2.7</b> Truncation, censoring, and constraints</a></li>
<li class="chapter" data-level="5.2.8" data-path="cha-writing-models.html"><a href="cha-writing-models.html#subsec:macros"><i class="fa fa-check"></i><b>5.2.8</b> Model macros</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="6" data-path="cha-building-models.html"><a href="cha-building-models.html"><i class="fa fa-check"></i><b>6</b> Building and using models</a>
<ul>
<li class="chapter" data-level="6.1" data-path="cha-building-models.html"><a href="cha-building-models.html#creating-model-objects"><i class="fa fa-check"></i><b>6.1</b> Creating model objects</a>
<ul>
<li class="chapter" data-level="6.1.1" data-path="cha-building-models.html"><a href="cha-building-models.html#using-nimblemodel-to-create-a-model"><i class="fa fa-check"></i><b>6.1.1</b> Using <em>nimbleModel</em> to create a model</a></li>
<li class="chapter" data-level="6.1.2" data-path="cha-building-models.html"><a href="cha-building-models.html#sec:readBUGSmodel"><i class="fa fa-check"></i><b>6.1.2</b> Creating a model from standard BUGS and JAGS input files</a></li>
<li class="chapter" data-level="6.1.3" data-path="cha-building-models.html"><a href="cha-building-models.html#sub:multiple-instances"><i class="fa fa-check"></i><b>6.1.3</b> Making multiple instances from the same model definition</a></li>
</ul></li>
<li class="chapter" data-level="6.2" data-path="cha-building-models.html"><a href="cha-building-models.html#sec:nodes-and-variables"><i class="fa fa-check"></i><b>6.2</b> NIMBLE models are objects you can query and manipulate</a>
<ul>
<li class="chapter" data-level="6.2.1" data-path="cha-building-models.html"><a href="cha-building-models.html#sec:what-are-nodes-and-variables"><i class="fa fa-check"></i><b>6.2.1</b> What are variables and nodes?</a></li>
<li class="chapter" data-level="6.2.2" data-path="cha-building-models.html"><a href="cha-building-models.html#determining-the-nodes-and-variables-in-a-model"><i class="fa fa-check"></i><b>6.2.2</b> Determining the nodes and variables in a model</a></li>
<li class="chapter" data-level="6.2.3" data-path="cha-building-models.html"><a href="cha-building-models.html#sec:accessing-nodes"><i class="fa fa-check"></i><b>6.2.3</b> Accessing nodes</a></li>
<li class="chapter" data-level="6.2.4" data-path="cha-building-models.html"><a href="cha-building-models.html#sec:how-nodes-are"><i class="fa fa-check"></i><b>6.2.4</b> How nodes are named</a></li>
<li class="chapter" data-level="6.2.5" data-path="cha-building-models.html"><a href="cha-building-models.html#sec:why-use-node"><i class="fa fa-check"></i><b>6.2.5</b> Why use node names?</a></li>
<li class="chapter" data-level="6.2.6" data-path="cha-building-models.html"><a href="cha-building-models.html#sec:cdisdata"><i class="fa fa-check"></i><b>6.2.6</b> Checking if a node holds data</a></li>
</ul></li>
<li class="chapter" data-level="6.3" data-path="cha-building-models.html"><a href="cha-building-models.html#using-models-in-parallel"><i class="fa fa-check"></i><b>6.3</b> Using models in parallel</a></li>
</ul></li>
<li class="part"><span><b>III Algorithms in NIMBLE</b></span></li>
<li class="chapter" data-level="7" data-path="cha-mcmc.html"><a href="cha-mcmc.html"><i class="fa fa-check"></i><b>7</b> MCMC</a>
<ul>
<li class="chapter" data-level="7.1" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:nimbleMCMC"><i class="fa fa-check"></i><b>7.1</b> One-line invocation of MCMC: <em>nimbleMCMC</em></a></li>
<li class="chapter" data-level="7.2" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:mcmc-configuration"><i class="fa fa-check"></i><b>7.2</b> The MCMC configuration</a>
<ul>
<li class="chapter" data-level="7.2.1" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:default-mcmc-conf"><i class="fa fa-check"></i><b>7.2.1</b> Default MCMC configuration</a></li>
<li class="chapter" data-level="7.2.2" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:customizing-mcmc-conf"><i class="fa fa-check"></i><b>7.2.2</b> Customizing the MCMC configuration</a></li>
<li class="chapter" data-level="7.2.3" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:derived-quantities"><i class="fa fa-check"></i><b>7.2.3</b> Setting up derived quantities for additional quantities of interest</a></li>
</ul></li>
<li class="chapter" data-level="7.3" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:build-compile-mcmc"><i class="fa fa-check"></i><b>7.3</b> Building and compiling the MCMC</a></li>
<li class="chapter" data-level="7.4" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:initMCMC"><i class="fa fa-check"></i><b>7.4</b> Initializing MCMC</a></li>
<li class="chapter" data-level="7.5" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:runMCMC"><i class="fa fa-check"></i><b>7.5</b> User-friendly execution of MCMC algorithms: <em>runMCMC</em></a></li>
<li class="chapter" data-level="7.6" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:executing-the-mcmc-algorithm"><i class="fa fa-check"></i><b>7.6</b> Running the MCMC</a>
<ul>
<li class="chapter" data-level="7.6.1" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:mcmc-rerun"><i class="fa fa-check"></i><b>7.6.1</b> Rerunning versus restarting an MCMC</a></li>
<li class="chapter" data-level="7.6.2" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:sampler-time"><i class="fa fa-check"></i><b>7.6.2</b> Measuring sampler computation times: <em>getTimes</em></a></li>
<li class="chapter" data-level="7.6.3" data-path="cha-mcmc.html"><a href="cha-mcmc.html#assessing-the-adaption-process-of-rw-and-rw_block-samplers"><i class="fa fa-check"></i><b>7.6.3</b> Assessing the adaption process of <em>RW</em> and <em>RW_block</em> samplers</a></li>
</ul></li>
<li class="chapter" data-level="7.7" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:extracting-samples"><i class="fa fa-check"></i><b>7.7</b> Extracting MCMC samples</a></li>
<li class="chapter" data-level="7.8" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:WAIC"><i class="fa fa-check"></i><b>7.8</b> Calculating WAIC</a></li>
<li class="chapter" data-level="7.9" data-path="cha-mcmc.html"><a href="cha-mcmc.html#k-fold-cross-validation"><i class="fa fa-check"></i><b>7.9</b> k-fold cross-validation</a></li>
<li class="chapter" data-level="7.10" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:rjmcmc"><i class="fa fa-check"></i><b>7.10</b> Variable selection using Reversible Jump MCMC</a>
<ul>
<li class="chapter" data-level="7.10.1" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:rjmcmc-indicator"><i class="fa fa-check"></i><b>7.10.1</b> Using indicator variables</a></li>
<li class="chapter" data-level="7.10.2" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:rjmcmc-no-indicator"><i class="fa fa-check"></i><b>7.10.2</b> Without indicator variables</a></li>
</ul></li>
<li class="chapter" data-level="7.11" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:samplers-provided"><i class="fa fa-check"></i><b>7.11</b> Samplers provided with NIMBLE</a>
<ul>
<li class="chapter" data-level="7.11.1" data-path="cha-mcmc.html"><a href="cha-mcmc.html#conjugate-gibbs-samplers"><i class="fa fa-check"></i><b>7.11.1</b> Conjugate (‘Gibbs’) samplers</a></li>
<li class="chapter" data-level="7.11.2" data-path="cha-mcmc.html"><a href="cha-mcmc.html#subsec:HMC"><i class="fa fa-check"></i><b>7.11.2</b> Hamiltonian Monte Carlo (HMC)</a></li>
<li class="chapter" data-level="7.11.3" data-path="cha-mcmc.html"><a href="cha-mcmc.html#particle-filter-samplers"><i class="fa fa-check"></i><b>7.11.3</b> Particle filter samplers</a></li>
<li class="chapter" data-level="7.11.4" data-path="cha-mcmc.html"><a href="cha-mcmc.html#customized-log-likelihood-evaluations-rw_llfunction-sampler"><i class="fa fa-check"></i><b>7.11.4</b> Customized log-likelihood evaluations: <em>RW_llFunction sampler</em></a></li>
</ul></li>
<li class="chapter" data-level="7.12" data-path="cha-mcmc.html"><a href="cha-mcmc.html#sec:mcmc-example-litters"><i class="fa fa-check"></i><b>7.12</b> Detailed MCMC example: <em>litters</em></a></li>
<li class="chapter" data-level="7.13" data-path="cha-mcmc.html"><a href="cha-mcmc.html#mcmc-suite-compare-mcmcs"><i class="fa fa-check"></i><b>7.13</b> Comparing different MCMCs with <em>compareMCMCs</em></a></li>
<li class="chapter" data-level="7.14" data-path="cha-mcmc.html"><a href="cha-mcmc.html#running-mcmc-chains-in-parallel"><i class="fa fa-check"></i><b>7.14</b> Running MCMC chains in parallel</a></li>
</ul></li>
<li class="chapter" data-level="8" data-path="cha-algos-provided.html"><a href="cha-algos-provided.html"><i class="fa fa-check"></i><b>8</b> Particle Filters, PMCMC, and MCEM</a>
<ul>
<li class="chapter" data-level="8.1" data-path="cha-algos-provided.html"><a href="cha-algos-provided.html#particle-filters-sequential-monte-carlo-and-iterated-filtering"><i class="fa fa-check"></i><b>8.1</b> Particle filters / sequential Monte Carlo and iterated filtering</a>
<ul>
<li class="chapter" data-level="8.1.1" data-path="cha-algos-provided.html"><a href="cha-algos-provided.html#filtering-algorithms"><i class="fa fa-check"></i><b>8.1.1</b> Filtering algorithms</a></li>
<li class="chapter" data-level="8.1.2" data-path="cha-algos-provided.html"><a href="cha-algos-provided.html#sec:particle-mcmc"><i class="fa fa-check"></i><b>8.1.2</b> Particle MCMC (PMCMC)</a></li>
</ul></li>
<li class="chapter" data-level="8.2" data-path="cha-algos-provided.html"><a href="cha-algos-provided.html#monte-carlo-expectation-maximization-mcem"><i class="fa fa-check"></i><b>8.2</b> Monte Carlo Expectation Maximization (MCEM)</a>
<ul>
<li class="chapter" data-level="8.2.1" data-path="cha-algos-provided.html"><a href="cha-algos-provided.html#sec:estimate-mcem-cov"><i class="fa fa-check"></i><b>8.2.1</b> Estimating the asymptotic covariance From MCEM</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="9" data-path="cha-laplace.html"><a href="cha-laplace.html"><i class="fa fa-check"></i><b>9</b> Laplace, AGHQ, and nested approximations</a>
<ul>
<li class="chapter" data-level="9.1" data-path="cha-laplace.html"><a href="cha-laplace.html#sec:AD-laplace"><i class="fa fa-check"></i><b>9.1</b> Laplace approximation and adaptive Gauss-Hermite quadrature (AGHQ)</a>
<ul>
<li class="chapter" data-level="9.1.1" data-path="cha-laplace.html"><a href="cha-laplace.html#glmm-example"><i class="fa fa-check"></i><b>9.1.1</b> GLMM example</a></li>
<li class="chapter" data-level="9.1.2" data-path="cha-laplace.html"><a href="cha-laplace.html#using-laplace-approximation"><i class="fa fa-check"></i><b>9.1.2</b> Using Laplace approximation</a></li>
<li class="chapter" data-level="9.1.3" data-path="cha-laplace.html"><a href="cha-laplace.html#using-the-laplace-approximation-methods-directly"><i class="fa fa-check"></i><b>9.1.3</b> Using the Laplace approximation methods directly</a></li>
<li class="chapter" data-level="9.1.4" data-path="cha-laplace.html"><a href="cha-laplace.html#changing-the-optimization-methods"><i class="fa fa-check"></i><b>9.1.4</b> Changing the optimization methods</a></li>
</ul></li>
<li class="chapter" data-level="9.2" data-path="cha-laplace.html"><a href="cha-laplace.html#sec:nested-approx"><i class="fa fa-check"></i><b>9.2</b> Nested approximation (INLA-like) methods</a>
<ul>
<li class="chapter" data-level="9.2.1" data-path="cha-laplace.html"><a href="cha-laplace.html#overview-of-the-methodology"><i class="fa fa-check"></i><b>9.2.1</b> Overview of the methodology</a></li>
<li class="chapter" data-level="9.2.2" data-path="cha-laplace.html"><a href="cha-laplace.html#using-nimbles-nested-approximation"><i class="fa fa-check"></i><b>9.2.2</b> Using NIMBLE’s nested approximation</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="10" data-path="cha-spatial.html"><a href="cha-spatial.html"><i class="fa fa-check"></i><b>10</b> Spatial models</a>
<ul>
<li class="chapter" data-level="10.1" data-path="cha-spatial.html"><a href="cha-spatial.html#intrinsic-gaussian-car-model-dcar_normal"><i class="fa fa-check"></i><b>10.1</b> Intrinsic Gaussian CAR model: <em>dcar_normal</em></a>
<ul>
<li class="chapter" data-level="10.1.1" data-path="cha-spatial.html"><a href="cha-spatial.html#specification-and-density"><i class="fa fa-check"></i><b>10.1.1</b> Specification and density</a></li>
<li class="chapter" data-level="10.1.2" data-path="cha-spatial.html"><a href="cha-spatial.html#example"><i class="fa fa-check"></i><b>10.1.2</b> Example</a></li>
</ul></li>
<li class="chapter" data-level="10.2" data-path="cha-spatial.html"><a href="cha-spatial.html#proper-gaussian-car-model-dcar_proper"><i class="fa fa-check"></i><b>10.2</b> Proper Gaussian CAR model: <em>dcar_proper</em></a>
<ul>
<li class="chapter" data-level="10.2.1" data-path="cha-spatial.html"><a href="cha-spatial.html#specification-and-density-1"><i class="fa fa-check"></i><b>10.2.1</b> Specification and density</a></li>
<li class="chapter" data-level="10.2.2" data-path="cha-spatial.html"><a href="cha-spatial.html#example-1"><i class="fa fa-check"></i><b>10.2.2</b> Example</a></li>
</ul></li>
<li class="chapter" data-level="10.3" data-path="cha-spatial.html"><a href="cha-spatial.html#sec:spatial-mcmc-sampling-car"><i class="fa fa-check"></i><b>10.3</b> MCMC Sampling of CAR models</a>
<ul>
<li class="chapter" data-level="10.3.1" data-path="cha-spatial.html"><a href="cha-spatial.html#initial-values"><i class="fa fa-check"></i><b>10.3.1</b> Initial values</a></li>
<li class="chapter" data-level="10.3.2" data-path="cha-spatial.html"><a href="cha-spatial.html#zero-neighbor-regions"><i class="fa fa-check"></i><b>10.3.2</b> Zero-neighbor regions</a></li>
<li class="chapter" data-level="10.3.3" data-path="cha-spatial.html"><a href="cha-spatial.html#zero-mean-constraint"><i class="fa fa-check"></i><b>10.3.3</b> Zero-mean constraint</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="11" data-path="cha-bnp.html"><a href="cha-bnp.html"><i class="fa fa-check"></i><b>11</b> Bayesian nonparametric models</a>
<ul>
<li class="chapter" data-level="11.1" data-path="cha-bnp.html"><a href="cha-bnp.html#sec:bnpmixtures"><i class="fa fa-check"></i><b>11.1</b> Bayesian nonparametric mixture models</a></li>
<li class="chapter" data-level="11.2" data-path="cha-bnp.html"><a href="cha-bnp.html#sec:crp"><i class="fa fa-check"></i><b>11.2</b> Chinese Restaurant Process model</a>
<ul>
<li class="chapter" data-level="11.2.1" data-path="cha-bnp.html"><a href="cha-bnp.html#specification-and-density-2"><i class="fa fa-check"></i><b>11.2.1</b> Specification and density</a></li>
<li class="chapter" data-level="11.2.2" data-path="cha-bnp.html"><a href="cha-bnp.html#sec:excrp"><i class="fa fa-check"></i><b>11.2.2</b> Example</a></li>
<li class="chapter" data-level="11.2.3" data-path="cha-bnp.html"><a href="cha-bnp.html#sec:extensionscrp"><i class="fa fa-check"></i><b>11.2.3</b> Extensions</a></li>
</ul></li>
<li class="chapter" data-level="11.3" data-path="cha-bnp.html"><a href="cha-bnp.html#sec:sb"><i class="fa fa-check"></i><b>11.3</b> Stick-breaking model</a>
<ul>
<li class="chapter" data-level="11.3.1" data-path="cha-bnp.html"><a href="cha-bnp.html#specification-and-function"><i class="fa fa-check"></i><b>11.3.1</b> Specification and function</a></li>
<li class="chapter" data-level="11.3.2" data-path="cha-bnp.html"><a href="cha-bnp.html#sec:exsb"><i class="fa fa-check"></i><b>11.3.2</b> Example</a></li>
</ul></li>
<li class="chapter" data-level="11.4" data-path="cha-bnp.html"><a href="cha-bnp.html#mcmc-sampling-of-bnp-models"><i class="fa fa-check"></i><b>11.4</b> MCMC sampling of BNP models</a>
<ul>
<li class="chapter" data-level="11.4.1" data-path="cha-bnp.html"><a href="cha-bnp.html#sec:mcmcdcrp"><i class="fa fa-check"></i><b>11.4.1</b> Sampling CRP models</a></li>
<li class="chapter" data-level="11.4.2" data-path="cha-bnp.html"><a href="cha-bnp.html#sec:mcmcsb"><i class="fa fa-check"></i><b>11.4.2</b> Sampling stick-breaking models</a></li>
</ul></li>
</ul></li>
<li class="part"><span><b>IV Programming with NIMBLE</b></span></li>
<li class="chapter" data-level="" data-path="overview.html"><a href="overview.html"><i class="fa fa-check"></i>Overview</a></li>
<li class="chapter" data-level="12" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html"><i class="fa fa-check"></i><b>12</b> Writing simple nimbleFunctions</a>
<ul>
<li class="chapter" data-level="12.1" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:RC-intro"><i class="fa fa-check"></i><b>12.1</b> Introduction to simple nimbleFunctions</a></li>
<li class="chapter" data-level="12.2" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:r-fiunctions-implemented"><i class="fa fa-check"></i><b>12.2</b> R functions (or variants) implemented in NIMBLE</a>
<ul>
<li class="chapter" data-level="12.2.1" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#finding-help-for-nimbles-versions-of-r-functions"><i class="fa fa-check"></i><b>12.2.1</b> Finding help for NIMBLE’s versions of R functions</a></li>
<li class="chapter" data-level="12.2.2" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#basic-operations"><i class="fa fa-check"></i><b>12.2.2</b> Basic operations</a></li>
<li class="chapter" data-level="12.2.3" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:basic-math-linear"><i class="fa fa-check"></i><b>12.2.3</b> Math and linear algebra</a></li>
<li class="chapter" data-level="12.2.4" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:nimble-dist-funs"><i class="fa fa-check"></i><b>12.2.4</b> Distribution functions</a></li>
<li class="chapter" data-level="12.2.5" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:basic-flow-control"><i class="fa fa-check"></i><b>12.2.5</b> Flow control: <em>if-then-else</em>, <em>for</em>, <em>while</em>, and <em>stop</em></a></li>
<li class="chapter" data-level="12.2.6" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:print"><i class="fa fa-check"></i><b>12.2.6</b> <em>print</em> and <em>cat</em></a></li>
<li class="chapter" data-level="12.2.7" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:check-user-interr"><i class="fa fa-check"></i><b>12.2.7</b> Checking for user interrupts: <em>checkInterrupt</em></a></li>
<li class="chapter" data-level="12.2.8" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#optimization-optim-and-nimoptim"><i class="fa fa-check"></i><b>12.2.8</b> Optimization: <em>optim</em> and <em>nimOptim</em></a></li>
<li class="chapter" data-level="12.2.9" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#integration-integrate-and-nimintegrate"><i class="fa fa-check"></i><b>12.2.9</b> Integration: <em>integrate</em> and <em>nimIntegrate</em></a></li>
<li class="chapter" data-level="12.2.10" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:altern-keyw-some"><i class="fa fa-check"></i><b>12.2.10</b> ‘nim’ synonyms for some functions</a></li>
</ul></li>
<li class="chapter" data-level="12.3" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:how-nimble-handles"><i class="fa fa-check"></i><b>12.3</b> How NIMBLE handles types of variables</a>
<ul>
<li class="chapter" data-level="12.3.1" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:nimbleList-RCFuns"><i class="fa fa-check"></i><b>12.3.1</b> nimbleList data structures</a></li>
<li class="chapter" data-level="12.3.2" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:how-types-work"><i class="fa fa-check"></i><b>12.3.2</b> How numeric types work</a></li>
</ul></li>
<li class="chapter" data-level="12.4" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:decl-argum-return"><i class="fa fa-check"></i><b>12.4</b> Declaring argument and return types</a></li>
<li class="chapter" data-level="12.5" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:comp-nimbl-pass"><i class="fa fa-check"></i><b>12.5</b> Compiled nimbleFunctions pass arguments by reference</a></li>
<li class="chapter" data-level="12.6" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:calling-external-code"><i class="fa fa-check"></i><b>12.6</b> Calling external compiled code</a></li>
<li class="chapter" data-level="12.7" data-path="cha-RCfunctions.html"><a href="cha-RCfunctions.html#sec:calling-R-code"><i class="fa fa-check"></i><b>12.7</b> Calling uncompiled R functions from compiled nimbleFunctions</a></li>
</ul></li>
<li class="chapter" data-level="13" data-path="cha-user-defined.html"><a href="cha-user-defined.html"><i class="fa fa-check"></i><b>13</b> Creating user-defined distributions and functions for models</a>
<ul>
<li class="chapter" data-level="13.1" data-path="cha-user-defined.html"><a href="cha-user-defined.html#sec:user-functions"><i class="fa fa-check"></i><b>13.1</b> User-defined functions</a></li>
<li class="chapter" data-level="13.2" data-path="cha-user-defined.html"><a href="cha-user-defined.html#sec:user-distributions"><i class="fa fa-check"></i><b>13.2</b> User-defined distributions</a>
<ul>
<li class="chapter" data-level="13.2.1" data-path="cha-user-defined.html"><a href="cha-user-defined.html#sec:registerDistributions"><i class="fa fa-check"></i><b>13.2.1</b> Using <em>registerDistributions</em> for alternative parameterizations and providing other information</a></li>
</ul></li>
<li class="chapter" data-level="13.3" data-path="cha-user-defined.html"><a href="cha-user-defined.html#sec:adv-user-def"><i class="fa fa-check"></i><b>13.3</b> Advanced user-defined functions and distributions</a></li>
<li class="chapter" data-level="13.4" data-path="cha-user-defined.html"><a href="cha-user-defined.html#sec:user-macros"><i class="fa fa-check"></i><b>13.4</b> User-defined model macros</a></li>
</ul></li>
<li class="chapter" data-level="14" data-path="cha-using-models.html"><a href="cha-using-models.html"><i class="fa fa-check"></i><b>14</b> Working with NIMBLE models</a>
<ul>
<li class="chapter" data-level="14.1" data-path="cha-using-models.html"><a href="cha-using-models.html#sec:accessing-variables"><i class="fa fa-check"></i><b>14.1</b> The variables and nodes in a NIMBLE model</a>
<ul>
<li class="chapter" data-level="14.1.1" data-path="cha-using-models.html"><a href="cha-using-models.html#sec:get-nodes"><i class="fa fa-check"></i><b>14.1.1</b> Determining the nodes in a model</a></li>
<li class="chapter" data-level="14.1.2" data-path="cha-using-models.html"><a href="cha-using-models.html#sec:introduced-nodes"><i class="fa fa-check"></i><b>14.1.2</b> Understanding lifted nodes</a></li>
<li class="chapter" data-level="14.1.3" data-path="cha-using-models.html"><a href="cha-using-models.html#sec:cdgetdependencies"><i class="fa fa-check"></i><b>14.1.3</b> Determining dependencies in a model</a></li>
</ul></li>
<li class="chapter" data-level="14.2" data-path="cha-using-models.html"><a href="cha-using-models.html#sec:nodeInfo"><i class="fa fa-check"></i><b>14.2</b> Accessing information about nodes and variables</a>
<ul>
<li class="chapter" data-level="14.2.1" data-path="cha-using-models.html"><a href="cha-using-models.html#getting-distributional-information-about-a-node"><i class="fa fa-check"></i><b>14.2.1</b> Getting distributional information about a node</a></li>
<li class="chapter" data-level="14.2.2" data-path="cha-using-models.html"><a href="cha-using-models.html#getting-information-about-a-distribution"><i class="fa fa-check"></i><b>14.2.2</b> Getting information about a distribution</a></li>
<li class="chapter" data-level="14.2.3" data-path="cha-using-models.html"><a href="cha-using-models.html#sec:getParam"><i class="fa fa-check"></i><b>14.2.3</b> Getting distribution parameter values for a node</a></li>
<li class="chapter" data-level="14.2.4" data-path="cha-using-models.html"><a href="cha-using-models.html#sec:getBound"><i class="fa fa-check"></i><b>14.2.4</b> Getting distribution bounds for a node</a></li>
</ul></li>
<li class="chapter" data-level="14.3" data-path="cha-using-models.html"><a href="cha-using-models.html#sec:cdcalc-cdsim-cdgetl"><i class="fa fa-check"></i><b>14.3</b> Carrying out model calculations</a>
<ul>
<li class="chapter" data-level="14.3.1" data-path="cha-using-models.html"><a href="cha-using-models.html#core-model-operations-calculation-and-simulation"><i class="fa fa-check"></i><b>14.3.1</b> Core model operations: calculation and simulation</a></li>
<li class="chapter" data-level="14.3.2" data-path="cha-using-models.html"><a href="cha-using-models.html#sec:cdsimn-cdcalcn-cdget"><i class="fa fa-check"></i><b>14.3.2</b> Pre-defined nimbleFunctions for operating on model nodes: <em>simNodes</em>, <em>calcNodes</em>, and <em>getLogProbNodes</em></a></li>
<li class="chapter" data-level="14.3.3" data-path="cha-using-models.html"><a href="cha-using-models.html#sec:access-log-prob"><i class="fa fa-check"></i><b>14.3.3</b> Accessing log probabilities via <em>logProb</em> variables</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="15" data-path="cha-data-structures.html"><a href="cha-data-structures.html"><i class="fa fa-check"></i><b>15</b> Data structures in NIMBLE</a>
<ul>
<li class="chapter" data-level="15.1" data-path="cha-data-structures.html"><a href="cha-data-structures.html#sec:modelValues-struct"><i class="fa fa-check"></i><b>15.1</b> The modelValues data structure</a>
<ul>
<li class="chapter" data-level="15.1.1" data-path="cha-data-structures.html"><a href="cha-data-structures.html#creating-modelvalues-objects"><i class="fa fa-check"></i><b>15.1.1</b> Creating modelValues objects</a></li>
<li class="chapter" data-level="15.1.2" data-path="cha-data-structures.html"><a href="cha-data-structures.html#sec:access-cont-modelv"><i class="fa fa-check"></i><b>15.1.2</b> Accessing contents of modelValues</a></li>
</ul></li>
<li class="chapter" data-level="15.2" data-path="cha-data-structures.html"><a href="cha-data-structures.html#sec:nimbleLists"><i class="fa fa-check"></i><b>15.2</b> The nimbleList data structure</a>
<ul>
<li class="chapter" data-level="15.2.1" data-path="cha-data-structures.html"><a href="cha-data-structures.html#sec:predef-nimbleLists"><i class="fa fa-check"></i><b>15.2.1</b> Pre-defined nimbleList types</a></li>
<li class="chapter" data-level="15.2.2" data-path="cha-data-structures.html"><a href="cha-data-structures.html#sec:eigen-nimFunctions"><i class="fa fa-check"></i><b>15.2.2</b> Using <em>eigen</em> and <em>svd</em> in nimbleFunctions</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="16" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html"><i class="fa fa-check"></i><b>16</b> Writing nimbleFunctions to interact with models</a>
<ul>
<li class="chapter" data-level="16.1" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#sec:writ-nimble-funct"><i class="fa fa-check"></i><b>16.1</b> Overview</a></li>
<li class="chapter" data-level="16.2" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#sec:using-comp-nimbl"><i class="fa fa-check"></i><b>16.2</b> Using and compiling nimbleFunctions</a></li>
<li class="chapter" data-level="16.3" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#writing-setup-code"><i class="fa fa-check"></i><b>16.3</b> Writing setup code</a>
<ul>
<li class="chapter" data-level="16.3.1" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#useful-tools-for-setup-functions"><i class="fa fa-check"></i><b>16.3.1</b> Useful tools for setup functions</a></li>
<li class="chapter" data-level="16.3.2" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#sec:access-modify-numer"><i class="fa fa-check"></i><b>16.3.2</b> Accessing and modifying numeric values from setup</a></li>
<li class="chapter" data-level="16.3.3" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#determining-numeric-types-in-nimblefunctions"><i class="fa fa-check"></i><b>16.3.3</b> Determining numeric types in nimbleFunctions</a></li>
<li class="chapter" data-level="16.3.4" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#sec:determ-pers-texttts"><i class="fa fa-check"></i><b>16.3.4</b> Control of setup outputs</a></li>
</ul></li>
<li class="chapter" data-level="16.4" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#sec:nimble-lang-comp"><i class="fa fa-check"></i><b>16.4</b> Writing run code</a>
<ul>
<li class="chapter" data-level="16.4.1" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#sec:driv-models:-calc"><i class="fa fa-check"></i><b>16.4.1</b> Driving models: <em>calculate</em>, <em>calculateDiff</em>, <em>simulate</em>, <em>getLogProb</em></a></li>
<li class="chapter" data-level="16.4.2" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#getting-and-setting-variable-and-node-values"><i class="fa fa-check"></i><b>16.4.2</b> Getting and setting variable and node values</a></li>
<li class="chapter" data-level="16.4.3" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#getting-parameter-values-and-node-bounds"><i class="fa fa-check"></i><b>16.4.3</b> Getting parameter values and node bounds</a></li>
<li class="chapter" data-level="16.4.4" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#sec:access-model-modelv"><i class="fa fa-check"></i><b>16.4.4</b> Using modelValues objects</a></li>
<li class="chapter" data-level="16.4.5" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#sec:using-model-variable"><i class="fa fa-check"></i><b>16.4.5</b> Using model variables and modelValues in expressions</a></li>
<li class="chapter" data-level="16.4.6" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#sec:incl-other-meth"><i class="fa fa-check"></i><b>16.4.6</b> Including other methods in a nimbleFunction</a></li>
<li class="chapter" data-level="16.4.7" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#sec:using-other-nimbl"><i class="fa fa-check"></i><b>16.4.7</b> Using other nimbleFunctions</a></li>
<li class="chapter" data-level="16.4.8" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#sec:virt-nimbl-nimbl"><i class="fa fa-check"></i><b>16.4.8</b> Virtual nimbleFunctions and nimbleFunctionLists</a></li>
<li class="chapter" data-level="16.4.9" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#character-objects"><i class="fa fa-check"></i><b>16.4.9</b> Character objects</a></li>
<li class="chapter" data-level="16.4.10" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#sec:user-defined-data"><i class="fa fa-check"></i><b>16.4.10</b> User-defined data structures</a></li>
</ul></li>
<li class="chapter" data-level="16.5" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#sec:user-samplers"><i class="fa fa-check"></i><b>16.5</b> Example: writing user-defined samplers to extend NIMBLE’s MCMC engine</a>
<ul>
<li class="chapter" data-level="16.5.1" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#user-defined-samplers-and-posterior-predictive-nodes"><i class="fa fa-check"></i><b>16.5.1</b> User-defined samplers and posterior predictive nodes</a></li>
</ul></li>
<li class="chapter" data-level="16.6" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#copying-nimblefunctions-and-nimble-models"><i class="fa fa-check"></i><b>16.6</b> Copying nimbleFunctions (and NIMBLE models)</a></li>
<li class="chapter" data-level="16.7" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#sec:debugging"><i class="fa fa-check"></i><b>16.7</b> Debugging nimbleFunctions</a></li>
<li class="chapter" data-level="16.8" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#timing-nimblefunctions-with-run.time"><i class="fa fa-check"></i><b>16.8</b> Timing nimbleFunctions with <em>run.time</em></a></li>
<li class="chapter" data-level="16.9" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#clearing-and-unloading-compiled-objects"><i class="fa fa-check"></i><b>16.9</b> Clearing and unloading compiled objects</a></li>
<li class="chapter" data-level="16.10" data-path="cha-progr-with-models.html"><a href="cha-progr-with-models.html#reducing-memory-usage"><i class="fa fa-check"></i><b>16.10</b> Reducing memory usage</a></li>
</ul></li>
<li class="part"><span><b>V Automatic Derivatives in NIMBLE</b></span></li>
<li class="chapter" data-level="17" data-path="cha-AD.html"><a href="cha-AD.html"><i class="fa fa-check"></i><b>17</b> Automatic Derivatives</a>
<ul>
<li class="chapter" data-level="17.1" data-path="cha-AD.html"><a href="cha-AD.html#sec:use-derivs"><i class="fa fa-check"></i><b>17.1</b> How to turn on derivatives in a model</a></li>
<li class="chapter" data-level="17.2" data-path="cha-AD.html"><a href="cha-AD.html#sec:AD-user-def"><i class="fa fa-check"></i><b>17.2</b> How to support derivatives in user-defined functions and distributions</a></li>
<li class="chapter" data-level="17.3" data-path="cha-AD.html"><a href="cha-AD.html#what-operations-are-and-arent-supported-for-ad"><i class="fa fa-check"></i><b>17.3</b> What operations are and aren’t supported for AD</a></li>
<li class="chapter" data-level="17.4" data-path="cha-AD.html"><a href="cha-AD.html#basics-of-obtaining-derivatives-in-nimblefunctions"><i class="fa fa-check"></i><b>17.4</b> Basics of obtaining derivatives in <code>nimbleFunctions</code></a>
<ul>
<li class="chapter" data-level="17.4.1" data-path="cha-AD.html"><a href="cha-AD.html#checking-derivatives-with-uncompiled-execution"><i class="fa fa-check"></i><b>17.4.1</b> Checking derivatives with uncompiled execution</a></li>
<li class="chapter" data-level="17.4.2" data-path="cha-AD.html"><a href="cha-AD.html#sec:AD-holding-out"><i class="fa fa-check"></i><b>17.4.2</b> Holding some local variables out of derivative tracking</a></li>
<li class="chapter" data-level="17.4.3" data-path="cha-AD.html"><a href="cha-AD.html#sec:AD-multiple-NF"><i class="fa fa-check"></i><b>17.4.3</b> Using AD with multiple nimbleFunctions</a></li>
<li class="chapter" data-level="17.4.4" data-path="cha-AD.html"><a href="cha-AD.html#sec:understanding-more-AD"><i class="fa fa-check"></i><b>17.4.4</b> Understanding more about how AD works: <em>taping</em> of operations</a></li>
<li class="chapter" data-level="17.4.5" data-path="cha-AD.html"><a href="cha-AD.html#resetting-a-nimderivs-call"><i class="fa fa-check"></i><b>17.4.5</b> Resetting a <code>nimDerivs</code> call</a></li>
<li class="chapter" data-level="17.4.6" data-path="cha-AD.html"><a href="cha-AD.html#a-note-on-performance-benchmarking"><i class="fa fa-check"></i><b>17.4.6</b> A note on performance benchmarking</a></li>
</ul></li>
<li class="chapter" data-level="17.5" data-path="cha-AD.html"><a href="cha-AD.html#advanced-uses-double-taping"><i class="fa fa-check"></i><b>17.5</b> Advanced uses: double taping</a></li>
<li class="chapter" data-level="17.6" data-path="cha-AD.html"><a href="cha-AD.html#derivatives-involving-model-calculations"><i class="fa fa-check"></i><b>17.6</b> Derivatives involving model calculations</a>
<ul>
<li class="chapter" data-level="17.6.1" data-path="cha-AD.html"><a href="cha-AD.html#method-1-nimderivs-of-modelcalculate"><i class="fa fa-check"></i><b>17.6.1</b> Method 1: <code>nimDerivs</code> of <code>model$calculate</code></a></li>
<li class="chapter" data-level="17.6.2" data-path="cha-AD.html"><a href="cha-AD.html#method-2-nimderivs-of-a-method-that-calls-modelcalculate"><i class="fa fa-check"></i><b>17.6.2</b> Method 2: <code>nimDerivs</code> of a method that calls <code>model$calculate</code></a></li>
</ul></li>
<li class="chapter" data-level="17.7" data-path="cha-AD.html"><a href="cha-AD.html#sec:parameter-transform"><i class="fa fa-check"></i><b>17.7</b> Parameter transformations</a></li>
</ul></li>
<li class="chapter" data-level="18" data-path="example-maximum-likelihood-estimation-using-optim-with-gradients-from-nimderivs..html"><a href="example-maximum-likelihood-estimation-using-optim-with-gradients-from-nimderivs..html"><i class="fa fa-check"></i><b>18</b> Example: maximum likelihood estimation using <code>optim</code> with gradients from <code>nimDerivs</code>.</a></li>
<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
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<div id="cha-RCfunctions" class="section level1 hasAnchor" number="12">
<h1><span class="header-section-number">Chapter 12</span> Writing simple nimbleFunctions<a href="cha-RCfunctions.html#cha-RCfunctions" class="anchor-section" aria-label="Anchor link to header"></a></h1>
<div id="sec:RC-intro" class="section level2 hasAnchor" number="12.1">
<h2><span class="header-section-number">12.1</span> Introduction to simple nimbleFunctions<a href="cha-RCfunctions.html#sec:RC-intro" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p><em>nimbleFunctions</em> are the heart of programming in NIMBLE. In this
chapter, we introduce simple nimbleFunctions that contain only one
function to be executed, in either compiled or uncompiled form, but no
setup function or additional methods.</p>
<p>Defining a simple nimbleFunction is like defining an R function:
<code>nimbleFunction</code> returns a function that can be executed, and it
can also be compiled. Simple nimbleFunctions are useful for doing math or the other
kinds of processing available in NIMBLE when no model or modelValues
is needed. These can be used for any purpose in R programming. They
can also be used as new functions and distributions in NIMBLE’s
extension of BUGS (Chapter <a href="cha-user-defined.html#cha-user-defined">13</a>).</p>
<p>Here’s a basic example implementing the textbook calculation of
least squares estimation of linear regression parameters<a href="#fn21" class="footnote-ref" id="fnref21"><sup>21</sup></a>:</p>
<div class="sourceCode" id="cb371"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb371-1"><a href="cha-RCfunctions.html#cb371-1" tabindex="-1"></a>solveLeastSquares <span class="ot"><-</span> <span class="fu">nimbleFunction</span>(</span>
<span id="cb371-2"><a href="cha-RCfunctions.html#cb371-2" tabindex="-1"></a> <span class="at">run =</span> <span class="cf">function</span>(<span class="at">X =</span> <span class="fu">double</span>(<span class="dv">2</span>), <span class="at">y =</span> <span class="fu">double</span>(<span class="dv">1</span>)) { <span class="co"># type declarations</span></span>
<span id="cb371-3"><a href="cha-RCfunctions.html#cb371-3" tabindex="-1"></a> ans <span class="ot"><-</span> <span class="fu">inverse</span>(<span class="fu">t</span>(X) <span class="sc">%*%</span> X) <span class="sc">%*%</span> (<span class="fu">t</span>(X) <span class="sc">%*%</span> y)</span>
<span id="cb371-4"><a href="cha-RCfunctions.html#cb371-4" tabindex="-1"></a> <span class="fu">return</span>(ans)</span>
<span id="cb371-5"><a href="cha-RCfunctions.html#cb371-5" tabindex="-1"></a> <span class="fu">returnType</span>(<span class="fu">double</span>(<span class="dv">2</span>)) <span class="co"># return type declaration</span></span>
<span id="cb371-6"><a href="cha-RCfunctions.html#cb371-6" tabindex="-1"></a> } )</span>
<span id="cb371-7"><a href="cha-RCfunctions.html#cb371-7" tabindex="-1"></a></span>
<span id="cb371-8"><a href="cha-RCfunctions.html#cb371-8" tabindex="-1"></a>X <span class="ot"><-</span> <span class="fu">matrix</span>(<span class="fu">rnorm</span>(<span class="dv">400</span>), <span class="at">nrow =</span> <span class="dv">100</span>)</span>
<span id="cb371-9"><a href="cha-RCfunctions.html#cb371-9" tabindex="-1"></a>y <span class="ot"><-</span> <span class="fu">rnorm</span>(<span class="dv">100</span>)</span>
<span id="cb371-10"><a href="cha-RCfunctions.html#cb371-10" tabindex="-1"></a><span class="fu">solveLeastSquares</span>(X, y)</span></code></pre></div>
<pre><code>## [,1]
## [1,] 0.088547575
## [2,] 0.002025635
## [3,] -0.090387283
## [4,] -0.072660391</code></pre>
<div class="sourceCode" id="cb373"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb373-1"><a href="cha-RCfunctions.html#cb373-1" tabindex="-1"></a>CsolveLeastSquares <span class="ot"><-</span> <span class="fu">compileNimble</span>(solveLeastSquares)</span>
<span id="cb373-2"><a href="cha-RCfunctions.html#cb373-2" tabindex="-1"></a><span class="fu">CsolveLeastSquares</span>(X, y)</span></code></pre></div>
<pre><code>## [,1]
## [1,] 0.088547575
## [2,] 0.002025635
## [3,] -0.090387283
## [4,] -0.072660391</code></pre>
<p>In this example, we fit a linear model for 100 random response values (<code>y</code>) to four columns of
randomly generated explanatory variables (<code>X</code>). We ran the
nimbleFunction
<code>solveLeastSquares</code> uncompiled,
natively in R, allowing testing and debugging (Section <a href="cha-progr-with-models.html#sec:debugging">16.7</a>). Then we compiled it and showed that the compiled version does the same thing,
but faster<a href="#fn22" class="footnote-ref" id="fnref22"><sup>22</sup></a>. NIMBLE’s compiler creates C++ that uses the Eigen (<a href="http://eigen.tuxfamily.org">http://eigen.tuxfamily.org</a>)
library for linear algebra.</p>
<p>Notice that the actual NIMBLE code is written as an R function
definition that is passed to <code>nimbleFunction</code> as the <code>run</code>
argument. Hence we call it the <em>run</em> code. run code is
written in the NIMBLE language. This is similar to a narrow subset of
R with some additional features. Formally, we view it as a distinct language
that encompasses what can be compiled from a nimbleFunction.</p>
<p>To write nimbleFunctions, you will need to learn:</p>
<ul>
<li>what R functions are supported for NIMBLE compilation and any
ways they differ from their regular R counterparts;</li>
<li>how NIMBLE handles types of variables;</li>
<li>how to declare types of <code>nimbleFunction</code> arguments and return values;</li>
<li>that compiled nimbleFunctions always pass arguments to each
other by reference.
<!--- 1. how to use nimbleList data structures. --></li>
</ul>
<p>The next sections cover each of these topics in turn.</p>
</div>
<div id="sec:r-fiunctions-implemented" class="section level2 hasAnchor" number="12.2">
<h2><span class="header-section-number">12.2</span> R functions (or variants) implemented in NIMBLE<a href="cha-RCfunctions.html#sec:r-fiunctions-implemented" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<div id="finding-help-for-nimbles-versions-of-r-functions" class="section level3 hasAnchor" number="12.2.1">
<h3><span class="header-section-number">12.2.1</span> Finding help for NIMBLE’s versions of R functions<a href="cha-RCfunctions.html#finding-help-for-nimbles-versions-of-r-functions" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>Often, R help pages are available for NIMBLE’s versions of R functions
using the prefix ‘nim’ and capitalizing the next letter. For
example, help on NIMBLE’s version of <code>numeric</code> can be found by <code>help(nimNumeric)</code>. In some cases help is found directly using the name of the function as it appears in R.</p>
</div>
<div id="basic-operations" class="section level3 hasAnchor" number="12.2.2">
<h3><span class="header-section-number">12.2.2</span> Basic operations<a href="cha-RCfunctions.html#basic-operations" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>Basic R operations supported for NIMBLE compilation are listed in
Table <a href="cha-RCfunctions.html#tab:coreR">12.1</a>.</p>
<table>
<caption><span id="tab:coreR">Table 12.1: </span> Basic R manipulation functions in NIMBLE. For some of these functions, in addition to the usual use of <code>help()</code>, you can find help in R for NIMBLE’s version of a function by using the “nim” prefix and capitalizing the next letter. E.g. <code>help(nimC)</code> for help with <code>c()</code>.</caption>
<thead>
<tr class="header">
<th align="left">Function</th>
<th align="left">Comments (differences from R)</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left"><code>c()</code></td>
<td align="left">No <code>recursive</code> argument.</td>
</tr>
<tr class="even">
<td align="left"><code>rep()</code></td>
<td align="left">No <code>rep.int</code> or <code>rep_len</code> arguments.</td>
</tr>
<tr class="odd">
<td align="left"><code>seq()</code> and ‘:’</td>
<td align="left">Negative integer sequences from ‘:’, e.g. , <code>2:1</code> do not work.</td>
</tr>
<tr class="even">
<td align="left"><code>which()</code></td>
<td align="left">No <code>arr.ind</code> or <code>useNames</code> arguments.</td>
</tr>
<tr class="odd">
<td align="left"><code>diag()</code></td>
<td align="left">Works like R in three ways:</td>
</tr>
<tr class="even">
<td align="left"></td>
<td align="left"><code>diag(vector)</code> returns a matrix with <code>vector</code> on the diagonal;</td>
</tr>
<tr class="odd">
<td align="left"></td>
<td align="left"><code>diag(matrix)</code> returns the diagonal vector of <code>matrix</code>;</td>
</tr>
<tr class="even">
<td align="left"></td>
<td align="left"><code>diag(n)</code> returns an <span class="math inline">\(n \times n\)</span> identity matrix. No <code>nrow</code> or <code>ncol</code> arguments.</td>
</tr>
<tr class="odd">
<td align="left"><code>diag()<-</code></td>
<td align="left">Works for assigning the diagonal vector of a matrix.</td>
</tr>
<tr class="even">
<td align="left"><code>dim()</code></td>
<td align="left">Works on a vector as well as higher-dimensional arguments.</td>
</tr>
<tr class="odd">
<td align="left"><code>length()</code></td>
<td align="left"></td>
</tr>
<tr class="even">
<td align="left"><code>is.na()</code></td>
<td align="left">Does not correctly handle NAs (or NaNs) from R that are type <code>'logical'</code> or <code>'integer'</code>,</td>
</tr>
<tr class="odd">
<td align="left"></td>
<td align="left">so convert these using <code>as.numeric()</code> before passing from R to NIMBLE.</td>
</tr>
<tr class="even">
<td align="left"><code>is.nan()</code></td>
<td align="left"></td>
</tr>
<tr class="odd">
<td align="left"><code>any()</code></td>
<td align="left">One argument only; NAs treated as FALSE.</td>
</tr>
<tr class="even">
<td align="left"><code>all()</code></td>
<td align="left">One argument only; NAs treated as FALSE.</td>
</tr>
<tr class="odd">
<td align="left"><code>numeric()</code></td>
<td align="left">Allows additional arguments to control initialization.</td>
</tr>
<tr class="even">
<td align="left"><code>logical()</code></td>
<td align="left">Allows additional arguments to control initialization.</td>
</tr>
<tr class="odd">
<td align="left"><code>integer()</code></td>
<td align="left">Allows additional arguments to control initialization.</td>
</tr>
<tr class="even">
<td align="left"><code>matrix()</code></td>
<td align="left">Allows additional arguments to control initialization.</td>
</tr>
<tr class="odd">
<td align="left"><code>array()</code></td>
<td align="left">Allows additional arguments to control initialization.</td>
</tr>
<tr class="even">
<td align="left">indexing</td>
<td align="left">Arbitrary integer and logical indexing is supported for objects of one or two dimensions.</td>
</tr>
<tr class="odd">
<td align="left"></td>
<td align="left">For higher-dimensional objects, only <code>:</code> indexing works, and</td>
</tr>
<tr class="even">
<td align="left"></td>
<td align="left">then only to create an object of at most two dimensions.</td>
</tr>
</tbody>
</table>
<p>In addition to the above functions, we provide functions <code>any_na()</code> and <code>any_nan()</code> for finding if there are any <code>NA</code> or <code>NaN</code> values in a vector. These are equivalent to using <code>any(is.na())</code> and <code>any(is.nan())</code> in R, with the exception noted in the table above regarding <code>is.na()</code>.</p>
<p>Other R functions with numeric arguments and return value can be called during compiled execution by wrapping them as a <code>nimbleRcall</code> (see Section <a href="cha-RCfunctions.html#sec:calling-R-code">12.7</a>).</p>
<p>Next we cover some of these functions in more detail.</p>
<div id="numeric-integer-logical-matrix-and-array" class="section level4 hasAnchor" number="12.2.2.1">
<h4><span class="header-section-number">12.2.2.1</span> <em>numeric</em>, <em>integer</em>, <em>logical</em>, <em>matrix</em> and <em>array</em><a href="cha-RCfunctions.html#numeric-integer-logical-matrix-and-array" class="anchor-section" aria-label="Anchor link to header"></a></h4>
<p><code>numeric</code>, <code>integer</code>, or <code>logical</code> will create a 1-dimensional vector of
floating-point (or ‘double’ [precision]), integer, or logical values, respectively. The <code>length</code> argument specifies the vector
length (default 0), and the <code>value</code> argument specifies the initial
value either as a scalar (used for all vector elements, with default
0) or a vector. If a vector and its length is not equal to <code>length</code>, the remaining values will be filled by R-style recycling if the <code>recycle</code> argument is <code>TRUE</code> (which is the default). The <code>init</code> argument specifies
whether or not to initialize the elements in compiled code (default <code>TRUE</code>). If
first use of the variable does not rely on initial values, using
<code>init = FALSE</code> will yield slightly more efficient performance.</p>
<p><code>matrix</code> creates a 2-dimensional matrix object of either floating-point (if
<code>type = "double"</code>, the default), integer (if <code>type = "integer"</code>), or logical (if <code>type = "logical"</code>) values.
As in R, <code>nrow</code> and <code>ncol</code> arguments specify the number of rows and columns, respectively.
The <code>value</code> and <code>init</code> arguments are used in the same way as for
<code>numeric</code>, <code>integer</code>, and <code>logical</code>.</p>
<p><code>array</code> creates a vector or higher-dimensional object, depending
on the <code>dim</code> argument, which takes a vector of sizes for each
dimension. The <code>type</code>, <code>value</code> and <code>init</code> argument behave
the same as for <code>matrix</code>.</p>
<p>The best way to create an identity matrix is with <code>diag(n)</code>, which
returns an <span class="math inline">\(n \times n\)</span> identity matrix. NIMBLE also provides a deprecated
nimbleFunction <code>identityMatrix</code> that does the same thing.</p>
<p>Examples of these functions, and the related function <span class="math inline">\(`setSize`\)</span>
for changing the size of a numeric object, are given in Section <a href="cha-RCfunctions.html#sec:chang-sizes-exist">12.3.2.4</a>.</p>
</div>
<div id="sec:query-chang-sizes" class="section level4 hasAnchor" number="12.2.2.2">
<h4><span class="header-section-number">12.2.2.2</span> <em>length</em> and <em>dim</em><a href="cha-RCfunctions.html#sec:query-chang-sizes" class="anchor-section" aria-label="Anchor link to header"></a></h4>
<p><code>length</code> behaves like R’s <code>length</code> function. It
returns the <em>entire</em> length of X. That means if <code>X</code> is
multivariate, <code>length(X)</code> returns the product of the sizes of
the dimensions. NIMBLE’s version of <code>dim</code>, which has synonym <code>nimDim</code>, behaves like R’s
<code>dim</code> function for matrices or arrays and like R’s
<code>length</code> function for vectors. In other words, regardless of
whether the number of dimensions is 1 or more, it returns a vector
of the sizes.</p>
</div>
<div id="deprecated-creation-of-non-scalar-objects-using-declare" class="section level4 hasAnchor" number="12.2.2.3">
<h4><span class="header-section-number">12.2.2.3</span> Deprecated creation of non-scalar objects using <em>declare</em><a href="cha-RCfunctions.html#deprecated-creation-of-non-scalar-objects-using-declare" class="anchor-section" aria-label="Anchor link to header"></a></h4>
<p>Previous versions of NIMBLE provided a function <code>declare</code> for
declaring variables. The more R-like functions <code>numeric</code>,
<code>integer</code>, <code>logical</code>, <code>matrix</code> and <code>array</code> are intended to replace
<code>declare</code>, but <code>declare</code> is still supported for backward
compatibility. In a future version of NIMBLE, <code>declare</code> may be removed.</p>
</div>
</div>
<div id="sec:basic-math-linear" class="section level3 hasAnchor" number="12.2.3">
<h3><span class="header-section-number">12.2.3</span> Math and linear algebra<a href="cha-RCfunctions.html#sec:basic-math-linear" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>Numeric scalar and matrix mathematical operations are listed in Tables <a href="cha-RCfunctions.html#tab:functions2">12.2</a>-<a href="cha-RCfunctions.html#tab:functionsMatrix2">12.3</a>.</p>
<!---
would need to do some sed manipulation to be able to automate this cross-ref
\@ref(tab:functions) and \@ref(tab:functionsMatrix).
-->
<p>As in R, many scalar operations in NIMBLE will work component-wise on vectors or
higher dimensional objects. For example if B and C are vectors, <code>A = B + C</code> will add them and create vector C by component-wise
addition of B and C. In the current version of NIMBLE, component-wise operations
generally only work for vectors and matrices, not arrays with more
than two dimensions. The only exception is assignment: <code>A = B</code> will
work up to NIMBLE’s current limit of four dimensions.</p>
<table>
<caption><span id="tab:functions2">Table 12.2: </span> Functions operating on scalars, many of which can operate on each element (component-wise) of
vectors and matrices. Status column indicates if the function is currently provided in NIMBLE. Vector input column
indicates if the function can take a vector as an argument (i.e., if the function is vectorized).</caption>
<thead>
<tr class="header">
<th align="left">Usage</th>
<th align="left">Description</th>
<th align="left">Comments</th>
<th>Status</th>
<th>Vector input</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left"><code>x | y</code>, <code>x & y</code></td>
<td align="left">logical OR (<span class="math inline">\(|\)</span>) and AND(&)</td>
<td align="left"></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>!x</code></td>
<td align="left">logical not</td>
<td align="left"></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="odd">
<td align="left"><code>x > y, x >= y</code></td>
<td align="left">greater than (and or equal to)</td>
<td align="left"></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>x < y, x <= y</code></td>
<td align="left">less than (and or equal to)</td>
<td align="left"></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="odd">
<td align="left"><code>x != y, x == y</code></td>
<td align="left">(not) equals</td>
<td align="left"></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>x + y, x - y, x * y</code></td>
<td align="left">component-wise operators</td>
<td align="left">mix of scalar and vector</td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="odd">
<td align="left"><code>x / y</code></td>
<td align="left">component-wise division</td>
<td align="left">vector <span class="math inline">\(x\)</span> and scalar <span class="math inline">\(y\)</span></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>x^y, pow(x, y)</code></td>
<td align="left">power</td>
<td align="left"><span class="math inline">\(x^y\)</span>; vector <span class="math inline">\(x\)</span>,scalar <span class="math inline">\(y\)</span></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="odd">
<td align="left"><code>x %% y</code></td>
<td align="left">modulo (remainder)</td>
<td align="left"></td>
<td>yes</td>
<td>no</td>
</tr>
<tr class="even">
<td align="left"><code>min(x1, x2),</code></td>
<td align="left">min. (max.) of two scalars</td>
<td align="left"></td>
<td>yes</td>
<td>See <code>pmin</code>,</td>
</tr>
<tr class="odd">
<td align="left"><code>max(x1, x2)</code></td>
<td align="left"></td>
<td align="left"></td>
<td></td>
<td><code>pmax</code></td>
</tr>
<tr class="even">
<td align="left"><code>exp(x)</code></td>
<td align="left">exponential</td>
<td align="left"></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="odd">
<td align="left"><code>log(x)</code></td>
<td align="left">natural logarithm</td>
<td align="left"></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>sqrt(x)</code></td>
<td align="left">square root</td>
<td align="left"></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="odd">
<td align="left"><code>abs(x)</code></td>
<td align="left">absolute value</td>
<td align="left"></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>step(x)</code></td>
<td align="left">step function at 0</td>
<td align="left">0 if <span class="math inline">\(x<0\)</span>, 1 if <span class="math inline">\(x>=0\)</span></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="odd">
<td align="left"><code>equals(x, y)</code></td>
<td align="left">equality of two scalars</td>
<td align="left">1 if <span class="math inline">\(x==y\)</span>, 0 if <span class="math inline">\(x != y\)</span></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>cube(x)</code></td>
<td align="left">third power</td>
<td align="left"><span class="math inline">\(x^3\)</span></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="odd">
<td align="left"><code>sin(x), cos(x),</code></td>
<td align="left">trigonometric functions</td>
<td align="left"></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>tan(x)</code></td>
<td align="left"></td>
<td align="left"></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td align="left"><code>asin(x), acos(x),</code></td>
<td align="left">inverse trigonometric functions</td>
<td align="left"></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>atan(x)</code></td>
<td align="left"></td>
<td align="left"></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td align="left"><code>asinh(x), acosh(x),</code></td>
<td align="left">inv. hyperbolic trig. functions</td>
<td align="left"></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>atanh(x)</code></td>
<td align="left"></td>
<td align="left"></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td align="left"><code>logit(x)</code></td>
<td align="left">logit</td>
<td align="left"><span class="math inline">\(\log(x/(1-x))\)</span></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>ilogit(x), expit(x)</code></td>
<td align="left">inverse logit</td>
<td align="left"><span class="math inline">\(\exp(x)/(1 + \exp(x))\)</span></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="odd">
<td align="left"><code>probit(x)</code></td>
<td align="left">probit (Gaussian quantile)</td>
<td align="left"><span class="math inline">\(\Phi^{-1}(x)\)</span></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>iprobit(x), phi(x)</code></td>
<td align="left">inverse probit (Gaussian CDF)</td>
<td align="left"><span class="math inline">\(\Phi(x)\)</span></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="odd">
<td align="left"><code>cloglog(x)</code></td>
<td align="left">complementary log log</td>
<td align="left"><span class="math inline">\(\log(-\log(1-x))\)</span></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>icloglog(x)</code></td>
<td align="left">inverse complementary log log</td>
<td align="left"><span class="math inline">\(1 - \exp(-\exp(x))\)</span></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="odd">
<td align="left"><code>ceiling(x)</code></td>
<td align="left">ceiling function</td>
<td align="left"><span class="math inline">\(\lceil(x)\rceil\)</span></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>floor(x)</code></td>
<td align="left">floor function</td>
<td align="left"><span class="math inline">\(\lfloor(x)\rfloor\)</span></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="odd">
<td align="left"><code>round(x)</code></td>
<td align="left">round to integer</td>
<td align="left"></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="even">
<td align="left"><code>trunc(x)</code></td>
<td align="left">truncation to integer</td>
<td align="left"></td>
<td>yes</td>
<td>yes</td>
</tr>
<tr class="odd">
<td align="left"><code>lgamma(x), loggam(x)</code></td>
<td align="left">log gamma function</td>