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author | Karl Berry <karl@freefriends.org> | 2015-09-29 22:08:57 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2015-09-29 22:08:57 +0000 |
commit | 6c088673b9f7d4b0e3b186b850d4fd6ba9997326 (patch) | |
tree | 3c86550ea260098612b6ca6f6f0250664a606716 /Master/texmf-dist/doc/latex/lstbayes/examples.tex | |
parent | 982ab23fae158d0e4ca19de74a6fa98928334007 (diff) |
lstbayes (29sep15)
git-svn-id: svn://tug.org/texlive/trunk@38498 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/lstbayes/examples.tex')
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diff --git a/Master/texmf-dist/doc/latex/lstbayes/examples.tex b/Master/texmf-dist/doc/latex/lstbayes/examples.tex new file mode 100644 index 00000000000..48a1c91be51 --- /dev/null +++ b/Master/texmf-dist/doc/latex/lstbayes/examples.tex @@ -0,0 +1,129 @@ +\documentclass{article} + +\title{Examples for the \textsf{lstbayes} package} +\author{Jeffrey B. Arnold} + +\usepackage{lstbayes} +\usepackage{hyperref} + +\begin{document} + +\maketitle{} + +Some example programs typset using the \textsf{listings} language drivers provideb by the \textsf{lstbayes} package. + +\section{BUGS} + +The Rats model from the OpenBUGS Examples Volume I: \url{http://www.openbugs.net/Examples/Rats.html}. +\begin{lstlisting}[language=BUGS] +model { + for( i in 1 : N ) { + for( j in 1 : T ) { + Y[i , j] ~ dnorm(mu[i , j],tau.c) + mu[i , j] <- alpha[i] + beta[i] * (x[j] - xbar) + culmative.Y[i , j] <- culmative(Y[i , j], Y[i , j]) + post.pv.Y[i , j] <- post.p.value(Y[i , j]) + prior.pv.Y[i , j] <- prior.p.value(Y[i , j]) + replicate.post.Y[i , j] <- replicate.post(Y[i , j]) + pv.post.Y[i , j] <- step(Y[i , j] - replicate.post.Y[i , j]) + replicate.prior.Y[i , j] <- replicate.prior(Y[i , j]) + pv.prior.Y[i , j] <- step(Y[i , j] - replicate.prior.Y[i , j]) + } + alpha[i] ~ dnorm(alpha.c,alpha.tau) + beta[i] ~ dnorm(beta.c,beta.tau) + } + tau.c ~ dgamma(0.001,0.001) + sigma <- 1 / sqrt(tau.c) + alpha.c ~ dnorm(0.0,1.0E-6) + alpha.tau ~ dgamma(0.001,0.001) + beta.c ~ dnorm(0.0,1.0E-6) + beta.tau ~ dgamma(0.001,0.001) + alpha0 <- alpha.c - xbar * beta.c +} +\end{lstlisting} + + +\section{JAGS} + +Linear regression example from John Myles White, \url{http://www.johnmyleswhite.com/notebook/2010/08/20/using-jags-in-r-with-the-rjags-package/}. + +\begin{lstlisting}[language=JAGS] +model { + for (i in 1:N){ + y[i] ~ dnorm(y.hat[i], tau) + y.hat[i] <- a + b * x[i] + } + a ~ dnorm(0, .0001) + b ~ dnorm(0, .0001) + tau <- pow(sigma, -2) + sigma ~ dunif(0, 100) +} +\end{lstlisting} + + +\section{Stan} + +Rats example from \url{https://github.com/stan-dev/example-models/blob/master/bugs_examples/vol1/rats/rats_vec.stan}. + +\begin{lstlisting}[language=Stan] +# http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/Vol1.pdf +# Page 3: Rats +data { + int<lower=0> N; + int<lower=0> T; + real x[T]; + real y[N,T]; + real xbar; +} +transformed data { + real x_minus_xbar[T]; + real y_linear[N*T]; + + for (t in 1:T) + x_minus_xbar[t] <- x[t] - xbar; + + for (n in 1:N) + for (t in 1:T) + y_linear[(n-1)*T + t] <- y[n, t]; +} +parameters { + real alpha[N]; + real beta[N]; + + real mu_alpha; + real mu_beta; + + real<lower=0> sigmasq_y; + real<lower=0> sigmasq_alpha; + real<lower=0> sigmasq_beta; +} +transformed parameters { + real<lower=0> sigma_y; + real<lower=0> sigma_alpha; + real<lower=0> sigma_beta; + + sigma_y <- sqrt(sigmasq_y); + sigma_alpha <- sqrt(sigmasq_alpha); + sigma_beta <- sqrt(sigmasq_beta); +} +model { + real pred[N*T]; + + for (n in 1:N) + for (t in 1:T) + pred[(n-1)*T + t] <- fma(beta[n], x_minus_xbar[t], alpha[n]); + + mu_alpha ~ normal(0, 100); + mu_beta ~ normal(0, 100); + sigmasq_y ~ inv_gamma(0.001, 0.001); + sigmasq_alpha ~ inv_gamma(0.001, 0.001); + sigmasq_beta ~ inv_gamma(0.001, 0.001); + alpha ~ normal(mu_alpha, sigma_alpha); // vectorized + beta ~ normal(mu_beta, sigma_beta); // vectorized + + y_linear ~ normal(pred, sigma_y); // vectorized +} +\end{lstlisting} + +\end{document} + |