[Pomp-commits] r1148 - www/vignettes

noreply at r-forge.r-project.org noreply at r-forge.r-project.org
Tue Mar 24 15:19:19 CET 2015 

Author: kingaa
Date: 2015-03-24 15:19:18 +0100 (Tue, 24 Mar 2015)
New Revision: 1148

Modified:
   www/vignettes/pomp.pdf
   www/vignettes/pompjss.R
   www/vignettes/pompjss.Rnw
   www/vignettes/pompjss.bib
   www/vignettes/pompjss.pdf
Log:
- update vignette

Modified: www/vignettes/pomp.pdf
===================================================================
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+++ www/vignettes/pomp.pdf	2015-03-24 14:19:18 UTC (rev 1148)
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Modified: www/vignettes/pompjss.R
===================================================================
--- www/vignettes/pompjss.R	2015-03-24 13:44:58 UTC (rev 1147)
+++ www/vignettes/pompjss.R	2015-03-24 14:19:18 UTC (rev 1148)
@@ -361,15 +361,15 @@
 ## ----gompertz-multi-mif-table,echo=F,results="asis"----------------------
 require(xtable)
 options(
-        xtable.sanitize.text.function=function(x)x,
-        xtable.floating=FALSE
-        )
+xtable.sanitize.text.function=function(x)x,
+xtable.floating=FALSE
+)
 print(xtable(results.table,align="r|cccccc",digits=c(0,4,4,4,2,2,2)))
 
 ## ----gompertz-dprior1,tidy=F---------------------------------------------
 hyperparams <- list(min = coef(gompertz)/10, max = coef(gompertz) * 10)
 
-## ----gompertz-dprior2----------------------------------------------------
+## ----gompertz-dprior2,tidy=FALSE-----------------------------------------
 gompertz.dprior <- function (params, ..., log) {
   f <- sum(dunif(params, min = hyperparams$min, max = hyperparams$max,
                  log = TRUE))
@@ -427,11 +427,11 @@
 rm(pmcmc1,save.seed,tic,toc)
 })
 
-## ----pmcmc-diagnostics,results="hide",fig.show="hide",echo=F-------------
-gelman.diag(pmcmc.traces)
-gelman.plot(pmcmc.traces)
-autocorr.plot(pmcmc.traces[[1]])
-hist(rle(unlist(pmcmc.traces[,"r"]))$length)
+## ----pmcmc-diagnostics,results="hide",fig.show="hide",echo=F,eval=F------
+## gelman.diag(pmcmc.traces)
+## gelman.plot(pmcmc.traces)
+## autocorr.plot(pmcmc.traces[[1]])
+## hist(rle(unlist(pmcmc.traces[,"r"]))$length)
 
 ## ----pmcmc-plot,echo=F,eval=T,results="hide",cache=TRUE------------------
 op <- par(mar=c(4,3.5,0,1),mfcol=c(3,2),mgp=c(2.5,1,0),cex.axis=1.5,cex.lab=2)
@@ -465,14 +465,12 @@
    Tr = exp(r);
    Tsigma = exp(sigma);
    Tphi = exp(phi);
-   TN_0 = exp(N_0);
-"
+   TN_0 = exp(N_0);"
 par.inv.trans <- "
    Tr = log(r);
    Tsigma = log(sigma);
    Tphi = log(phi);
-   TN_0 = log(N_0);
-"
+   TN_0 = log(N_0);"
 
 ## ----ricker-pomp,tidy=F--------------------------------------------------
 pomp(data = data.frame(time = seq(0, 50, by = 1), y = NA),
@@ -548,19 +546,19 @@
 })
 
 ## ----ricker-mif-calc,eval=FALSE,tidy=FALSE-------------------------------
-## mf <- mif(ricker,start=guess,Nmif=100,Np=1000,transform=TRUE,
-##           cooling.fraction=0.95^50,var.factor=2,ic.lag=3,
-##           rw.sd=c(r=0.1,sigma=0.1,phi=0.1),max.fail=50)
-## mf <- continue(mf,Nmif=500,max.fail=20)
+## mf <- mif(ricker, start = guess, Nmif = 100, Np = 1000, transform = TRUE,
+##           cooling.fraction = 0.95^50, var.factor = 2, ic.lag = 3,
+##           rw.sd=c(r = 0.1, sigma = 0.1, phi = 0.1), max.fail = 50)
+## mf <- continue(mf, Nmif = 500, max.fail = 20)
 
 ## ----ricker-mif-eval,echo=F,eval=T,cache=F,results="hide"----------------
 bake("ricker-mif.rda",{
   save.seed <- .Random.seed
   set.seed(718086921L)
-  mf <- mif(ricker,start=guess,Nmif=100,Np=1000,transform=TRUE,
-            cooling.fraction=0.95^50,var.factor=2,ic.lag=3,
-            rw.sd=c(r=0.1,sigma=0.1,phi=0.1),max.fail=50)
-  mf <- continue(mf,Nmif=500,max.fail=20)
+  mf <- mif(ricker, start = guess, Nmif = 100, Np = 1000, transform = TRUE,
+            cooling.fraction = 0.95^50, var.factor = 2, ic.lag = 3,
+            rw.sd=c(r = 0.1, sigma = 0.1, phi = 0.1), max.fail = 50)
+  mf <- continue(mf, Nmif = 500, max.fail = 20)
   .Random.seed <<- save.seed
 })
 

Modified: www/vignettes/pompjss.Rnw
===================================================================
--- www/vignettes/pompjss.Rnw	2015-03-24 13:44:58 UTC (rev 1147)
+++ www/vignettes/pompjss.Rnw	2015-03-24 14:19:18 UTC (rev 1148)
@@ -31,6 +31,8 @@
 \Crefname{appendix}{Appendix}{Appendices}
 \crefname{algorithm}{Algorithm}{Algorithms}
 \Crefname{algorithm}{Algorithm}{Algorithms}
+\crefname{section}{Section}{Sections}
+\Crefname{section}{Section}{Sections}
 \crefname{AlgoLine}{line}{lines}
 \Crefname{AlgoLine}{Line}{Lines}
 
@@ -218,6 +220,7 @@
 %% Note that you should use the \pkg{}, \proglang{} and \code{} commands.
 
 \section {Introduction}
+
 A partially observed Markov process (POMP) model consists of incomplete and noisy measurements of a latent, unobserved Markov process.
 The far-reaching applicability of this class of models has motivated much software development \citep{commandeur11}.
 It has been a challenge to provide a software environment that can effectively handle broad classes of POMP models and take advantage of the wide range of statistical methodologies that have been proposed for such models.
@@ -265,7 +268,8 @@
 Finally, \cref{sec:conclusion} discusses extensions and applications of \pkg{pomp}.
 
 
-\section[POMP models and their representation in pomp]{POMP models and their representation in \pkg{pomp}}\label{sec:background}
+\section[POMP models and their representation in pomp]{POMP models and their representation in \pkg{pomp}}
+\label{sec:background}
 
 Let $\theta$ be a $p$-dimensional real-valued parameter, $\theta\in\R^p$.
 For each value of $\theta$, let $\{X(t\giventh\theta),t\in T\}$ be a Markov process,
@@ -286,7 +290,8 @@
 Note that this formalism allows the transition density, $f_{X_{n}|X_{n-1}}$, and measurement density, $f_{Y_{n}|X_{n}}$, to depend explicitly on $n$.
 
 
-\subsection{Implementation of POMP models}\label{sec:implementation}
+\subsection{Implementation of POMP models}
+\label{sec:implementation}
 
 \pkg{pomp} is fully object-oriented:
 in the package, a POMP model is represented by an S4 object \citep{Chambers1998,genolini08} of \class{pomp}.
@@ -295,30 +300,32 @@
 \Cref{tab:notation} gives the mathematical notation corresponding to the elementary methods that can be executed on a \class{pomp} object.
 
 \begin{table}[t]
-  \begin{tabular}{llll}
-\hline
-Method &Argument to the &Mathematical terminology \\
-& \code{pomp} constructor & \\
-\hline
-\code{rprocess} &\code{rprocess} &Simulate from $f_{X_n|X_{n-1}}( x_n \given x_{n-1}\giventh \theta)$\\
-\code{dprocess} &\code{dprocess} &Evaluate $f_{X_n|X_{n-1}}( x_n \given x_{n-1}\giventh \theta)$\\
-\code{rmeasure} &\code{rmeasure} &Simulate from $f_{Y_n|X_n}( y_n \given x_n\giventh \theta)$\\
-\code{dmeasure} &\code{dmeasure} &Evaluate $f_{Y_n|X_n}( y_n \given x_n\giventh \theta)$\\
-\code{rprior} &\code{rprior} &Simulate from the prior distribution $\pi(\theta)$\\
-\code{dprior} &\code{dprior} &Evaluate the prior density $\pi(\theta)$\\
-\code{init.state} &\code{initializer} &Simulate from $f_{X_0}( x_0 \giventh \theta)$\\
-\code{timezero} &\code{t0} &$t_0$\\
-\code{time} &\code{times} &$t_{1:N}$\\
-\code{obs} &\code{data} &$y^*_{1:N}$\\
-\code{states} & --- &$x_{0:N}$\\
-\code{coef} &\code{params} &$\theta$\\
-\hline
-\end{tabular}
-\caption{
-  Constituent methods for \class{pomp} objects and their translation into mathematical notation for POMP models.
-  For example, the \code{rprocess} method is set using the \code{rprocess} argument to the \code{pomp} constructor function.
-}
-\label{tab:notation}
+  \begin{center}
+    \begin{tabular}{llll}
+      \hline
+      Method &Argument to the &Mathematical terminology \\
+      & \code{pomp} constructor & \\
+      \hline
+      \code{rprocess} &\code{rprocess} &Simulate from $f_{X_n|X_{n-1}}( x_n \given x_{n-1}\giventh \theta)$\\
+      \code{dprocess} &\code{dprocess} &Evaluate $f_{X_n|X_{n-1}}( x_n \given x_{n-1}\giventh \theta)$\\
+      \code{rmeasure} &\code{rmeasure} &Simulate from $f_{Y_n|X_n}( y_n \given x_n\giventh \theta)$\\
+      \code{dmeasure} &\code{dmeasure} &Evaluate $f_{Y_n|X_n}( y_n \given x_n\giventh \theta)$\\
+      \code{rprior} &\code{rprior} &Simulate from the prior distribution $\pi(\theta)$\\
+      \code{dprior} &\code{dprior} &Evaluate the prior density $\pi(\theta)$\\
+      \code{init.state} &\code{initializer} &Simulate from $f_{X_0}( x_0 \giventh \theta)$\\
+      \code{timezero} &\code{t0} &$t_0$\\
+      \code{time} &\code{times} &$t_{1:N}$\\
+      \code{obs} &\code{data} &$y^*_{1:N}$\\
+      \code{states} & --- &$x_{0:N}$\\
+      \code{coef} &\code{params} &$\theta$\\
+      \hline
+    \end{tabular}
+  \end{center}
+  \caption{
+    Constituent methods for \class{pomp} objects and their translation into mathematical notation for POMP models.
+    For example, the \code{rprocess} method is set using the \code{rprocess} argument to the \code{pomp} constructor function.
+    \label{tab:notation}
+  }
 \end{table}
 
 The \code{rprocess}, \code{dprocess}, \code{rmeasure}, and \code{dmeasure} arguments specify the transition probabilities $f_{X_n|X_{n-1}}( x_n \given x_{n-1}\giventh \theta)$ and measurement densities $f_{Y_n|X_n}(y_n\given x_n\giventh \theta)$.
@@ -365,7 +372,8 @@
 The \code{covar} argument in the \pkg{pomp} constructor allows for time-varying covariates measured at times specified in the \code{tcovar} argument.
 A example using covariates is given in \cref{sec:EpidemicModel}.
 
-\section{Methodology for POMP models}\label{sec:methods}
+\section{Methodology for POMP models}
+\label{sec:methods}
 
 Data analysis typically involves identifying regions of parameter space within which a postulated model is statistically consistent with the data.
 Additionally, one frequently desires to assess the relative merits of alternative models as explanations of the data.
@@ -384,59 +392,59 @@
 Though \pkg{pomp} has sufficient flexibility to encode arbitrary POMP models and methods and therefore also provides a platform for the development of novel POMP inference methodology,
 \pkg{pomp}'s development to date has focused on plug-and-play methods.
 However, the package developers welcome contributions and collaborations to further expand \pkg{pomp}'s functionality in non-plug-and-play directions also.
-In the remainder of this Section, we describe and discuss several inference methods, all currently implemented in the package.
+In the remainder of this section, we describe and discuss several inference methods, all currently implemented in the package.
 
 \begin{table}[t]
-\begin{tabular}{l|p{0.35\linewidth}|p{0.35\linewidth}}
-\multicolumn{3}{l}{\bf (a) Plug-and-play \rule[-2mm]{0mm}{4mm}  }\tabularnewline
-\hline
-&Frequentist   & Bayesian  \tabularnewline
-\hline
-Full information&
-Iterated filtering (\code{mif}, \cref{sec:mif}) \raggedright
-&PMCMC (\code{pmcmc}, \cref{sec:pmcmc}) \raggedright \tabularnewline
-\hline
-Feature-based
-&Nonlinear forecasting (\code{nlf}, \cref{sec:nlf}), \raggedright
-&ABC (\code{abc}, \cref{sec:abc}) \raggedright \tabularnewline
-&synthetic likelihood (\code{probe.match}, \cref{sec:probe}) \raggedright
-& \tabularnewline
-\hline
-\multicolumn{3}{c}{}\tabularnewline
-\multicolumn{3}{l}{\bf (b) Not plug-and-play \rule[-2mm]{0mm}{4mm}} \tabularnewline
-\hline
-& Frequentist         & Bayesian  \tabularnewline
-\hline
-Full information
-& EM and Monte~Carlo~EM,  \raggedright
-& MCMC \raggedright \tabularnewline
-& Kalman filter \raggedright
-& \tabularnewline
-\hline
-Feature-based
-&Trajectory matching (\code{traj.match}),  \raggedright
-& Extended Kalman filter \tabularnewline
-&extended Kalman filter,  \raggedright
-& \tabularnewline
-&Yule-Walker equations  \raggedright
-& \tabularnewline
-\hline
-\end{tabular}
-\caption{
-  Inference methods for POMP models.
-  For those currently implemented in \pkg{pomp}, function name and a reference for  description are provided in parentheses.
-  Standard Expectation-Maximization (EM) and Markov chain Monte~Carlo (MCMC) algorithms are not plug-and-play since they require evaluation of $f_{X_n|X_{n-1}}(x_n\given x_{n-1}\giventh\theta)$.
-  The Kalman filter and extended Kalman filter are not plug-and-play since they cannot be implemented based on a model simulator.
-  The Kalman filter provides the likelihood for a linear, Gaussian model.
-  The extended Kalman filter employs a local linear Gaussian approximation which can be used for frequentist inference (via maximization of the resulting quasi-likelihood) or approximate Bayesian inference (by adding the parameters to the state vector).
-  The Yule-Walker equations for ARMA models provide an example of a closed-form method of moments estimator.
-}
-\label{tab:methods}
+  \begin{tabular}{l|p{0.35\linewidth}|p{0.35\linewidth}}
+    \multicolumn{3}{l}{\bf (a) Plug-and-play \rule[-2mm]{0mm}{4mm}  }\tabularnewline
+    \hline
+    &Frequentist   & Bayesian  \tabularnewline
+    \hline
+    Full information&
+    Iterated filtering (\code{mif}, \cref{sec:mif}) \raggedright
+    &PMCMC (\code{pmcmc}, \cref{sec:pmcmc}) \raggedright \tabularnewline
+    \hline
+    Feature-based
+    &Nonlinear forecasting (\code{nlf}, \cref{sec:nlf}), \raggedright
+    &ABC (\code{abc}, \cref{sec:abc}) \raggedright \tabularnewline
+    &synthetic likelihood (\code{probe.match}, \cref{sec:probe}) \raggedright
+    & \tabularnewline
+    \hline
+    \multicolumn{3}{c}{}\tabularnewline
+    \multicolumn{3}{l}{\bf (b) Not plug-and-play \rule[-2mm]{0mm}{4mm}} \tabularnewline
+    \hline
+    & Frequentist         & Bayesian  \tabularnewline
+    \hline
+    Full information
+    & EM and Monte~Carlo~EM,  \raggedright
+    & MCMC \raggedright \tabularnewline
+    & Kalman filter \raggedright
+    & \tabularnewline
+    \hline
+    Feature-based
+    &Trajectory matching (\code{traj.match}),  \raggedright
+    & Extended Kalman filter \tabularnewline
+    &extended Kalman filter,  \raggedright
+    & \tabularnewline
+    &Yule-Walker equations  \raggedright
+    & \tabularnewline
+    \hline
+  \end{tabular}
+  \caption{
+    Inference methods for POMP models.
+    For those currently implemented in \pkg{pomp}, function name and a reference for  description are provided in parentheses.
+    Standard Expectation-Maximization (EM) and Markov chain Monte~Carlo (MCMC) algorithms are not plug-and-play since they require evaluation of $f_{X_n|X_{n-1}}(x_n\given x_{n-1}\giventh\theta)$.
+    The Kalman filter and extended Kalman filter are not plug-and-play since they cannot be implemented based on a model simulator.
+    The Kalman filter provides the likelihood for a linear, Gaussian model.
+    The extended Kalman filter employs a local linear Gaussian approximation which can be used for frequentist inference (via maximization of the resulting quasi-likelihood) or approximate Bayesian inference (by adding the parameters to the state vector).
+    The Yule-Walker equations for ARMA models provide an example of a closed-form method of moments estimator.
+  }
+  \label{tab:methods}
 \end{table}
 
+\subsection{The likelihood function and sequential Monte Carlo}
+\label{sec:pfilter}
 
-\subsection{The likelihood function and sequential Monte Carlo}\label{sec:pfilter}
-
 %%%%  PFILTER PSEUDOCODE
 \begin{algorithm}[ht]
   \caption{\textbf{Sequential Monte Carlo (SMC, or particle filter)}:
@@ -541,9 +549,11 @@
 In particular, if all the particle weights are equal then \cref{alg:systematic} has the appropriate behavior of leaving the particles unchanged.
 As pointed out by \citep{douc05}, stratified resampling performs better than multinomial sampling and \cref{alg:systematic} is in practice comparable in performance to stratified resampling and somewhat faster. 
 
+\pagebreak
 
 %%% ITERATED FILTERING
-\subsection{Iterated filtering}\label{sec:mif}
+\subsection{Iterated filtering}
+\label{sec:mif}
 
 % MIF PSEUDOCODE
 \begin{algorithm}[h]
@@ -631,7 +641,8 @@
 This approach has been used in a variety of previously proposed POMP methodologies \citep{kitagawa98,janeliu01,wan00} but iterated filtering is distinguished by having theoretical justification for convergence to the maximum likelihood estimate \citep{ionides11}.
 
 
-\subsection{Particle Markov chain Monte Carlo}\label{sec:pmcmc}
+\subsection{Particle Markov chain Monte Carlo}
+\label{sec:pmcmc}
 
 %% PMCMC PSEUDOCODE
 \begin{algorithm}[h]
@@ -680,7 +691,8 @@
 In part because it gains only a single likelihood evaluation from each particle-filtering operation, PMCMC can be computationally relatively inefficient \citep{bhadra10,ionides15}.
 Nevertheless, its invention introduced the possibility of full-information plug-and-play Bayesian inferences in some situations where they had been unavailable.
 
-\subsection{Synthetic likelihood of summary statistics}\label{sec:probe}
+\subsection{Synthetic likelihood of summary statistics}
+\label{sec:probe}
 
 %%%%% SYNTHETIC LIKELIHOOD EVALUATION ALGORITHM
 \begin{algorithm}
@@ -823,7 +835,8 @@
 the package supports alternative choices of proposal distribution.
 
 
-\subsection{Nonlinear forecasting} \label{sec:nlf}
+\subsection{Nonlinear forecasting}
+\label{sec:nlf}
 
 %%%%% NLF QUASI LIKELIHOOD ALGORITHM %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{algorithm}[h]
@@ -904,9 +917,12 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\section{Model construction and data analysis: simple examples} \label{sec:examples}
+%% \clearpage
+\section{Model construction and data analysis: Simple examples}
+\label{sec:examples}
 
-\subsection{A first example: the Gompertz model}\label{sec:gompertz:setup}
+\subsection{A first example: The Gompertz model}
+\label{sec:gompertz:setup}
 
 The plug-and-play methods in \pkg{pomp} were designed to facilitate data analysis based on complicated models, but we will first demonstrate the basics of \pkg{pomp} using simple discrete-time models, the Gompertz and Ricker models for population growth \citep{Reddingius1971,Ricker1954}.
 The Ricker model will be introduced in \cref{sec:ricker:setup} and used in \cref{sec:ricker:probe.match}; the remainder of \cref{sec:examples} will use the Gompertz model.
@@ -1129,7 +1145,8 @@
 The latter approach has the advantage of allowing one to estimate the Monte Carlo error itself;
 we will demonstrate this in \cref{sec:gompertz:mif}.
 
-\subsection{Maximum likelihood estimation via iterated filtering}\label{sec:gompertz:mif}
+\subsection{Maximum likelihood estimation via iterated filtering}
+\label{sec:gompertz:mif}
 
 Let us use the iterated filtering approach described in \cref{sec:mif} to obtain an approximate maximum likelihood estimate for the data in \code{gompertz}.
 Since the parameters of \cref{eq:gompertz1,eq:gompertz-obs} are constrained to be positive, when estimating, we transform them to a scale on which they are unconstrained.
@@ -1283,6 +1300,16 @@
 In this case, we see that the \code{mif} procedure is successfully maximizing the likelihood up to an error of about 0.1 log units.
 
 \begin{table}
[TRUNCATED]

To get the complete diff run:
    svnlook diff /svnroot/pomp -r 1148

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