Sibylle Sturtz Fachbereich Statistik UniversitЁat Dortmund Germany

Uwe Ligges Fachbereich Statistik UniversitЁat Dortmund Germany

Andrew Gelman Department of Statistics Columbia University USA

Abstract The R2OpenBUGS package provides convenient functions to call OpenBUGS from R. It automatically writes the data and scripts in a format readable by OpenBUGS for processing in batch mode, which is possible since version 1.4. After the OpenBUGS process has finished, it is possible either to read the resulting data into R by the package itself--which gives a compact graphical summary of inference and convergence diagnostics--or to use the facilities of the coda package for further analyses of the output. Examples are given to demonstrate the usage of this package. Keywords: R, OpenBUGS, interface, MCMC. An earlier version of this vignette has been published by the Journal of Statistical Software: Sturtz S, Ligges U, Gelman A (2005): "R2WinBUGS: A Package for Running WinBUGS from R." Journal of Statistical Software, 12(3), 116. R2OpenBUGS was adapted from R2WinBUGS by Neal Thomas. 1. Introduction The usage of Markov chain Monte Carlo (MCMC) methods became very popular within the last decade. OpenBUGS (Bayesian inference Using Gibbs Sampling, Spiegelhalter, Thomas, Best, and Lunn 2003) is a popular software for analyzing complex statistical models using MCMC methods. This software uses Gibbs sampling (Geman and Geman 1984; Gelfand and Smith 1990; Casella and George 1992) and the Metropolis algorithm (Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller 1953) to generate a Markov chain by sampling from full conditional distributions. The OpenBUGS software is available for free at http://www.OpenBUGS.info. An introduction to MCMC methods is given in Gilks, Richardson, and Spiegelhalter (1996). Using OpenBUGS, the user must specify the model to run, and to load data and initial values for a specified number of Markov chains. Then it is possible to run the Markov chain(s) and to save the results for the parameters the user is interested in. summary statistics of these data, convergence diagnostics, kernel estimates etc. are available as well. Nevertheless, some users of this software might be interested in saving the output and reading it into R (R Development Core Team 2004) for further analyses. OpenBUGS comes with the ability to run the software in batch mode using scripts. The R2OpenBUGS package makes use of this feature and provides the tools to call OpenBUGS directly after data manipulation in R. Furthermore, it is possible to work with the results after importing them back into R again, for example to create posterior predictive simulations or, more generally, graphical displays of data and posterior simulations (Gelman 2004). Embedding in R can also be useful for frequently changed data or processing a bunch of data sets, because it is much more convenient to use some R functions (possibly within a loop) rather than using "copy & [email protected] [email protected] [email protected]

2

R2OpenBUGS:A Package for Running OpenBUGS from R

paste" to update data in OpenBUGS each time; however difficulties have been encountered in this area because both R and OpenBUGS can lock up RAM in the Windows operating system. R is a "language for data analysis and graphics" and an open source and freely available statistical software package implementing that language, see http://www.R-project.org/. Historically, R is an implementation of the award-winning S language and system (Becker and Chambers 1984; Becker, Chambers, and Wilks 1988; Chambers and Hastie 1992; Chambers 1998). R and R2OpenBUGS are available from CRAN (Comprehensive R Archive Network), i.e., http: //CRAN.R-Project.org or one of its mirrors. R2OpenBUGS could be ported to the commercial S implementation S-Plus. Minor adaptions would be needed since S-Plus lacks some of R's functions and capabilities. If an Internet connection is available, R2OpenBUGS can be installed by typing install.packages("R2OpenBUGS") at the R command prompt. Do not forget to load the package with library("R2OpenBUGS"). The package coda by Plummer, Best, Cowles, and Vines (2004) is very useful for the analysis of OpenBUGS' output, the reader might want to install this package as well. The CRAN package boa (Bayesian Output Analysis Program) by Smith (2004) has similar aims. JAGS (Just Another Gibbs Sampler) by Plummer (2003) is a program for analysis of Bayesian hierarchical models using Gibbs sampling that aims for the same functionality as classic BUGS. JAGS is developed to work closely together with R and the coda package. In this paper, we give two examples, involving educational testing experiments in schools (cf. Section 2.1), and incidence of childhood leukaemia depending on benzene emissions (cf. Section 2.2). Details on the functions of R2OpenBUGS are given in Section 3. These functions automatically write the data and a script in a format readable by OpenBUGS for processing in batch mode, and call OpenBUGS from R. After the OpenBUGS process has finished, it is possible either to read the resulting data into R by the package itself or to use the facilities of the coda package for further analyses of the output. In Section 4, we demonstrate how to apply the functions provided by R2OpenBUGS on the examples' data, and how to analyze the output both with package coda and with R2OpenBUGS's methods to plot() and print() the output. 2. Examples In this Section, we introduce two examples which will be continued in Section 4. 2.1. Schools data The Scholastic Aptitude Test (SAT) measures the aptitude of high-schoolers in order to help colleges to make admissions decisions. It is divided into two parts, verbal (SAT-V) and mathematical (SAT-M). Our data comes from the SAT-V (Scholastic Aptitude Test-Verbal) on eight different high schools, from an experiment conducted in the late 1970s. SAT-V is a standard multiple choice test administered by the Educational Testing Service. This Service was interested in the effects of coaching programs for each of the selected schools. The study included coached and uncoached pupils, about sixty in each of the eight different schools; see Rubin (1981). All of them had already taken the PSAT (Preliminary SAT) which results were used as covariates. For each school, the estimated treatment effect and the standard error of the effect estimate are given. These are calculated by an analysis of covariance adjustment appropriate for a completely randomized experiment (Rubin 1981). This example was analyzed using a hierarchical normal model in Rubin (1981) and Gelman, Carlin, Stern, and Rubin (2003, Section 5.5). 2.2. Leukaemia registration data Spatial data usually arises on different, non-nesting spatial scales. One example is childhood leukaemia registration data analyzed by Best, Cockings, Bennett, Wakefield, and Elliott (2001) using ecologic regression. Data are given for Greater London bounded by the M25 orbital motorway. The data are not available as an example in R2OpenBUGS but we use the example here to illustrate alternative calls to the bugs() function and output analysis using the coda package.

Sibylle Sturtz, Uwe Ligges, Andrew Gelman

3

6 5 4 3 2 1 0 Figure 1: Observed number of cases of childhood leukaemia in 19851996

2

1

0 Figure 2: Expected number of cases of childhood leukaemia in 19851996 The observed number of leukaemia cases among children under 15 years old is given at ward level. Census wards are administrative areas containing approximately 5000 to 10 000 people. Central London is divided into 873 wards. The number of incident cases of leukaemia in children is available from 1985 until 1996 from the Office of national statistics and the Thames Cancer Registry. A plot of these numbers is given in Figure 1. Additionally, the number of expected cases (cf. Fig. 2) is calculated on the same resolution using population numbers for different age-sex-strata and the national leukaemia rate for the corresponding strata, for details see Best et al. (2001). It is assumed that benzene emissions have an effect on the incidence rate of leukaemia. Benzene emission rates are available in tonnes per year from an atmospheric emissions inventory for London (Buckingham, Clewley, Hutchinson, Sadler, and Shah 1997) produced by the London Research Centre. They are provided at 1km Ч 1km grid cells, giving 2132 grid cells in total. Their spatial distribution is shown in Figure 3. For further details on the data see Best et al. (2001). We model these data by Poisson-Gamma models introduced by Best, Ickstadt, and Wolpert (2000) using OpenBUGS. A linking matrix containing information which grid cell belongs to which ward

4

R2OpenBUGS:A Package for Running OpenBUGS from R

3 2 1 0 Figure 3: Benzene emissions in tonnes per year and to which amount is required. This matrix is calculated using R. Unfortunately, OpenBUGS does not support a list format such as directly produced by R. Therefore, the data must be provided as a matrix with 2132 rows and 873 columns (or vice versa). Most of the entries of this matrix are zeroes, but using dump() to export it from R yields in a file size of 14.2 MB. Unfortunately, opening a file of such size really slows OpenBUGS down, and it was not even possible on some of our PCs. Importing data written by our R2OpenBUGS package does not make any problems using the batch mode, probably due to memory management issues in OpenBUGS. 3. Implementation The implementation of the R2OpenBUGS package is straightforward. The "main" function bugs() is intended to be called by the user. In principle, it is a wrapper for several other functions called therein step by step as follows: 1. bugs.data.inits() writes the data files `data.txt', and `inits1.txt', `inits2.txt', ... into the working directory. These files will be used by OpenBUGS during batch processing. In particular, input for OpenBUGS must not exceed a certain number of digits. Moreover, it needs an E instead of an e in scientific notation. Scientific notation is particularly desirable because of the "number of digits" limitation. The default (digits = 5) is to, e.g., reformat the number 123456.789 to 1.23457E+05. 2. bugs.script() writes the file `script.txt' that is used by OpenBUGS for batch processing. 3. bugs.run() updates the lengths of the adaptive phases in the WinBUGS registry (using a function bugs.update.settings()), calls WinBUGS, and runs it in batch mode with `script.txt'. 4. bugs.sims() is only called if the argument codaPkg has been set to FALSE (the default). Otherwise bugs() returns the filenames of stored data. These can, for example, be imported by package coda (see the example in Section 4.2, page 10), which provides functions for convergence diagnostics, calculation of Monte Carlo estimates, trace plots, and so forth. The function bugs.sims() reads simulations from OpenBUGS into R (not necessarily called by bugs() itself), formats them, monitors convergence, performs convergence checks, and computes medians and quantiles. It also prepares the output for bugs() itself.

Sibylle Sturtz, Uwe Ligges, Andrew Gelman

5

These functions are not intended to be called by the user directly. Arguments are passed from bugs() to the other functions, if appropriate. A shortened help file of bugs() listing all arguments is given in Appendix A; for the full version type ?bugs in R after having installed and loaded the package R2OpenBUGS (see Section 1). As known from OpenBUGS, one must specify the data in form of a list, with list names equal to the names of data in the corresponding OpenBUGS model. Alternatively, it is possible to specify a vector or list of names (of mode character). In that case objects of that names are looked for in the environment in which bugs() has been called (usually that is the user's Workspace, .GlobalEnv). If data have already been written in a file called `data.txt' to the working directory, it is possible to specify data = "data.txt". One will usually want to supply initial values. This can be done either in the form of a function inits() that creates these values, so that different chains can be automatically initialized at different points (see Section 4.1), or by specifying them directly (see Section 4.2). If inits() is not specified, bugs() just uses the starting values created by OpenBUGS; but in practice OpenBUGS can crash when reasonable initial values are not specified, and so we recommend constructing a simple inits() function to simulate reasonable starting points (Gelman et al. 2003, Section C.2). It is also necessary to specify which parameters should be saved for monitoring by specifying parameters.to.save. The user might also want to change the defaults for the length of the burn-in (n.burnin, which defaults to half the length of the chain) period for every MCMC run and the number of iterations (n.iter, default value 3) that are used to calculate Monte Carlo estimates. The specification of a thinning parameter (n.thin) is possible as well; this is useful when the number of parameters is large, to keep the saved output to a reasonably-sized R object. By setting the argument debug = TRUE, OpenBUGS remains open after the run. This way it is possible to find errors in the code or the data structure, or even to work with that software as in a usual run. This feature is not available with Linux execution. It is possible to run one or more Markov chains. The number of chains (n.chains) must be specified together with the chains' initial values (inits). If more than one Markov chain is requested and codaPkg is set to FALSE, the convergence diagnostic R^ (Brooks and Gelman 1998) is calculated by bugs.sims() for each of the saved parameters. Since the communication between OpenBUGS and R is based on files, rather huge files will be saved in the working directory by the bugs() call, either files to be read in by bugs() itself, or by the coda package. The user might want to delete those files after the desired contents has been imported into R, and save those objects, e.g., as compressed R data files. The function bugs() returns a rather complex object of class bugs, if called with argument codaPkg = FALSE. In order to look at the structure of such an object, type str(objectname). For convenience, R2OpenBUGS provides methods corresponding to class bugs for the generic functions print() and plot(). So that user will not be overwhelmed with information; summaries of the output are provided by the print() method. That is, some parameters of the bugs() call are summarized, and mean, standard deviation, several quantiles of the parameters and convergence diagnostics based on Gelman and Rubin (1992) are printed. See the example in Section 4.1, page 7, for a typical output. As with Spiegelhalter, Best, Carlin, and van der Linde (2002), the DIC computed by bugs.sims() is defined as the posterior mean of the deviance plus pD, the estimated effective number of parameters in the posterior distribution. We define pD as half the posterior variance of the deviance and estimate it as half the average of the within-chain variances of the deviance.1 The plot() for objects of class bugs provides information condensed in some plots conveniently arranged within the same graphics device. For an example, see Figure 4 in Section 4.1. It is 1In contrast, Spiegelhalter et al. (2002), and OpenBUGS, define pD as the posterior mean of the deviance evaluated at the posterior mean of the parameter values. We cannot use that definition because the deviance function is not available to our program, which calls OpenBUGS from the "outside". Both definitions of pD--ours and that introduced by Spiegelhalter et al. (2002)--can be derived from the asymptotic 2 distribution of the deviance relative to its minimum (Gelman et al. 2003, Section 6.7). We make no claim that our measure of pD is superior to that of Spiegelhalter et al. (2002); we choose this measure purely because it is computationally possible given what is available to us from the OpenBUGS output.

6

R2OpenBUGS:A Package for Running OpenBUGS from R

intended to adapt this function to work with MCMC output in general, even if obtained from software other than OpenBUGS.

4. Examples continued The Examples introduced in Section 4 are continued in this Section. We apply the functions provided by R2OpenBUGS to the examples' data and analyze the output.

4.1. Schools data Schools example data (see Section 2.1) are available with the R2OpenBUGS package:

> data(schools)

> schools

school estimate

1

A 28.39

2

B 7.94

3

C -2.75

4

D 6.82

5

E -0.64

6

F 0.63

7

G 18.01

8

H 12.16

sd 14.9 10.2 16.3 11.0 9.4 11.4 10.4 17.6

For modeling these data, we use a hierarchical model as proposed by Gelman et al. (2003, Section 5.5). We assume a normal distribution for the observed estimate for each school with mean theta and inverse-variance tau.y. The inverse-variance is given as 1/sigma.y2 and its prior distribution is uniform on (0,1000). For the mean theta, we employ another normal distribution with mean mu.theta and inverse-variance tau.theta. For their prior distributions, see the following OpenBUGS code:

model { for (j in 1:J) { y[j] ~ dnorm (theta[j], tau.y[j]) theta[j] ~ dnorm (mu.theta, tau.theta) tau.y[j] <- pow(sigma.y[j], -2) } mu.theta ~ dnorm (0.0, 1.0E-6) tau.theta <- pow(sigma.theta, -2) sigma.theta ~ dunif (0, 1000) } This model must be stored in a separate file, e.g. `schools.bug'2, in an appropriate directory, say c:/schools/. In R the user must prepare the data inputs the bugs() function needs. This can be a list containing the name of each data vector, e.g. > J <- nrow(schools) > y <- schools$estimate > sigma.y <- schools$sd > data <- list ("J", "y", "sigma.y") 2Emacs Speaks Statistics (ESS) by Rossini, Heiberger, Sparapani, MЁachler, and Hornik (2004), a package available with Gnu Emacs (Stallmann 1999), recognizes and properly formats Bugs model files that have the .bug extension.

Sibylle Sturtz, Uwe Ligges, Andrew Gelman

7

Using these data and the model file, we can run an MCMC simulation to get estimates for theta, mu.theta and sigma.theta. Before running, the user must decide how many chains to be run (n.chain = 3) for how many iterations (n.iter = 1000). If the length of burn-in is not specified, n.burnin = floor(n.iter/2) is used, that is, 500 in this example. Additionally, the user must specify initial values for the chains, for example by writing a function. This can be done by

> inits <- function(){

+ list(theta = rnorm(J, 0, 100), mu.theta = rnorm(1, 0, 100),

+

sigma.theta = runif(1, 0, 100))

+}

Now, the user can start the MCMC simulation by typing

> schools.sim <- bugs(data, inits, model.file = "c:/schools/schools.bug",

+

parameters = c("theta", "mu.theta", "sigma.theta"),

+

n.chains = 3, n.iter = 1000)

in R. For other available arguments, see Appendix A. The results in objects schools.sim can conveniently be printed by print(schools.sim). The generic function print() calls the print method for an object of class bugs provided by R2OpenBUGS. For this example, you will get something like

> print(schools.sim) Inference for Bugs model at "c:/schools/schools.bug" 3 chains, each with 1000 iterations (first 500 discarded) n.sims = 1500 iterations saved mean sd 2.5% 25% 50% 75% 97.5% Rhat n.eff theta[1] 11.1 9.1 -3.0 5.0 10.0 16.0 31.8 1.1 39 theta[2] 7.6 6.6 -4.7 3.3 7.8 11.6 21.1 1.1 42 theta[3] 5.7 8.4 -12.5 0.6 6.1 10.8 21.8 1.0 150 theta[4] 7.1 7.0 -6.6 2.7 7.2 11.5 21.0 1.1 42 theta[5] 5.1 6.8 -9.5 0.7 5.2 9.7 18.1 1.0 83 theta[6] 5.7 7.3 -9.7 1.0 6.2 10.2 20.0 1.0 56 theta[7] 10.4 7.3 -2.1 5.3 9.8 15.3 25.5 1.1 27 theta[8] 8.3 8.4 -6.6 2.8 8.1 12.7 26.2 1.0 64 mu.theta 7.6 5.9 -3.0 3.7 8.0 11.0 19.5 1.1 35 sigma.theta 6.7 5.6 0.3 2.8 5.1 9.2 21.2 1.1 46 deviance 60.8 2.5 57.0 59.1 60.2 62.1 66.6 1.0 170 pD = 3 and DIC = 63.8 (using the rule, pD = var(deviance)/2)

For each parameter, n.eff is a crude measure of effective sample size, and Rhat is the potential scale reduction factor (at convergence, Rhat=1). DIC is an estimate of expected predictive error (lower deviance is better).

Additionally, the user can generate a plot of the results by typing plot(schools.sim). The resulting plot is given in Figure 4. In this plot, the left column shows a quick summary of inference and convergence (R is close to 1.0 for all parameters, indicating good mixing of the three chains and thus approximate convergence); and the right column shows inferences for each set of parameters. As can be seen in the right column, R2OpenBUGS uses the parameter names in OpenBUGS to structure the output into scalar, vector, and arrays of parameters, in addition to storing the parameters as a long vector. For the interpretation of these results see Gelman et al. (2003, Section 5.5).

4.2. Leukaemia registration data The leukaemia registration data (see Section 2.2) are used to show data modeling and output reading into R using the coda package. A simple model for these data looks as follows:

8

R2OpenBUGS:A Package for Running OpenBUGS from R

Bugs model at "c:/schools/schools.bug", 3 chains, each with 1000 iterations

80% interval for each chain R-hat -20 0 20 40 1 1.5 2+

theta[1]

q

[2]

q

[3]

q

[4]

q

[5]

q

[6]

q

[7]

q

[8]

q

mu.theta

q

sigma.theta

q

-20 0 20 40 1 1.5 2+

medians and 80% intervals

theta

40

20 0

q

q

q q

qq q

qq q

qq q

q q

q q

q q

q q

-20 12345678

20

10 qq

mu.theta

q

0

-10

20 sigma.theta10 q q q 0

65 q deviance 60 qq 55

Figure 4: Plot produced by R2OpenBUGS package for the schools example. model{ beta.0 ~ dgamma(a.0, tau.0) beta.benz ~ dgamma(a.benz, tau.benz) a.0 <- 0.575 tau.0 <- a.0*2 a.benz <- 0.575 tau.benz <- a.benz*2

Sibylle Sturtz, Uwe Ligges, Andrew Gelman

9

for (i in 1:I) { count[i] ~ dpois(lambda[i]) lambda[i] <- p[i]*expect[i] for (j in 1:J) { prop[j,i] <- gamma[j,i]*(benz[j] - benzbar) } p[i]<- beta.0 + beta.benz*sum(prop[,i]) } } Here count denotes the number of observed incidences of childhood leukaemia in ward i. These are assumed to be Poisson distributed with mean lambda depending on the number of expected cases expect in ward i and an area-specific risk rate p. For calculation of this area specific risk rate we use an intercept beta.0 and a term depending on the weighted sum of benzene emissions benz in each grid cell j. The weights are chosen proportional to the amount of area that ward i and grid cell j have in common. In R we can define all these data and then initialize the model. The data needed for this example are benzbar: arithmetic mean of all benzene values, benz: a vector containing benzene emissions of all 2132 grid cells, expect: expected number of cases of childhood leukaemia in each of the 873 wards, count: observed number of childhood leukaemia in these wards, gamma: a 2132 Ч 873 matrix containing the amount of area each grid cell and each ward have in common, J: total number of grid cells, i.e. 2132, and I: total number of ward cells, i.e. 873. The parameters we want to store are Regression Coefficients beta.0 and beta.benz as well as p, the area specific relative risk compared to the reference rate. This reference rate was used to calculate the expected number of cases in each ward. Since we want to use the coda package for reading the data into OpenBUGS, we specify codaPkg = TRUE in the bugs() call: > data <- list(benzbar = mean(benz), benz = benz, expect = expect, + count = count, gamma = gamma, J = J, I = I) > parameters <- c("beta.0", "beta.benz", "p") > inits1 <- list(beta.0 = 1, beta.benz = 1) > inits2 <- list(beta.0 = 0.5, beta.benz = 0.5) > inits <- list(inits1, inits2) > model <- bugs(data, inits, parameters, model.file = "c:/model.bug", + n.chains = 2, n.iter = 8000, n.burnin = 5000, n.thin = 1, + codaPkg = TRUE )

10

R2OpenBUGS:A Package for Running OpenBUGS from R

Starting with, e.g., > library("coda") > codaobject <- read.bugs(model) > plot(codaobject) it is now possible to use the coda package for output analyses. Acknowledgments The work of Uwe Ligges has been supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 475. The work of Andrew Gelman has been supported by the U.S. National Science Foundation. References Becker RA, Chambers JM (1984). S. An Interactive Environment for Data Analysis and Graphics. Wadsworth and Brooks/Cole, Monterey. Becker RA, Chambers JM, Wilks AR (1988). The NEW S Language -- A programming environment for Data Analysis and Graphics. Chapman & Hall, New York. Best NG, Cockings S, Bennett J, Wakefield J, Elliott P (2001). "Ecological Regression Analysis of Environmental Benzene Exposure and Childhood Leukaemia: Sensitivity to Data Inaccuracies, Geographical Scale and Ecological Bias." Journal of the Royal Statistical Society, Series A, 164, 155174. Best NG, Ickstadt K, Wolpert RL (2000). "Spatial Poisson Regression for Health and Exposure Data Measured at Disparate Resolutions." Journal of the American Statistical Association, 95, 10761088. Brooks SB, Gelman A (1998). "General Methods for Monitoring Convergence of Iterative Simulations." Journal of Computational and Graphical Statistics, 7, 434455. Buckingham C, Clewley L, Hutchinson D, Sadler L, Shah S (1997). "London Atmospheric Emissions Inventory." Technical report, London Research Centre, London. Casella G, George E (1992). "Explaining the Gibbs Sampler." American Statistician, 46, 167174. Chambers JM (1998). Programming with Data. A Guide to the S Language. Springer-Verlag, New York. Chambers JM, Hastie TJ (1992). Statistical Models in S. Chapman & Hall, New York. Gelfand AE, Smith AFM (1990). "Sampling-based Approaches to Calculating Marginal Densities." Journal of the American Statistical Association, 85, 398409. Gelman A (2004). "Exploratory Data Analysis for Complex Models (with Discussion)." Journal of Computational and Graphical Statistics, 13(4), 755779. Gelman A, Carlin J, Stern H, Rubin D (2003). Bayesian Data Analysis. CRC Press, Boca Raton, 2 edition. Gelman A, Rubin D (1992). "Inference from Iterative Simulation Using Multiple Sequences." Statistical Science, 7, 457511. Geman S, Geman D (1984). "Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images." IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721741.

Sibylle Sturtz, Uwe Ligges, Andrew Gelman

11

Gilks W, Richardson S, Spiegelhalter D (1996). Markov Chain Monte Carlo in Practice. Chapman & Hall, London. Metropolis N, Rosenbluth A, Rosenbluth M, Teller H, Teller E (1953). "Equation of State Calculations by Fast Computing Machines." Journal of Chemical Physics, 21, 10871092. Plummer M (2003). "JAGS: A Program for Analysis of Bayesian Graphical Models Using Gibbs Sampling." In K Hornik, F Leisch, A Zeileis (eds.), "Proceedings of the 3rd International Workshop on Distributed Statistical Computing, March 2022," Technische UniversitЁat Wien, Vienna. ISSN 1609-395X. URL http://www.ci.tuwien.ac.at/Conferences/ DSC-2003/Proceedings/. Plummer M, Best NG, Cowles K, Vines K (2004). coda: Output Analysis and Diagnostics for MCMC. R package version 0.9-1, URL http://www-fis.iarc.fr/coda/. R Development Core Team (2004). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http: //www.R-project.org. Rossini AJ, Heiberger RM, Sparapani RA, MЁachler M, Hornik K (2004). "Emacs Speaks Statistics: A Multiplatform, Multipackage Development Environment for statistical analysis." Journal of Computational and Graphical Statistics, 13(1), 247261. Rubin DB (1981). "Estimation in Parallel Randomized Experiments." Journal of Educational Statistics, 6, 377400. Smith BJ (2004). boa: Bayesian Output Analysis Program (BOA) for MCMC. R package version 1.1.2-1, URL http://www.public-health.uiowa.edu/boa. Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A (2002). "Bayesian Measures of Complexity and Fit." Journal of the Royal Statistical Society, SeriesB, 64, 583639. Spiegelhalter DJ, Thomas A, Best NG, Lunn D (2003). "WinBUGS Version 1.4 Users Manual." MRC Biostatistics Unit, Cambridge. URL http://www.mrc-bsu.cam.ac.uk/bugs/. Stallmann RM (1999). The Emacs Editor. Boston. Version 20.7, URL http://www.gnu.org/.

12

bugs

A. Help page for the function bugs() This help page has been shortened.

bugs

Run OpenBUGS from R

Description The bugs function takes data and starting values as input. It automatically writes a OpenBUGS script, calls the model, and saves the simulations for easy access in R.

Usage bugs(data, inits, parameters.to.save, n.iter, model.file="model.txt", n.chains=3, n.burnin=floor(n.iter / 2), n.thin=1, saveExec=FALSE,restart=FALSE, debug=FALSE, DIC=TRUE, digits=5, codaPkg=FALSE, OpenBUGS.pgm=NULL, working.directory=NULL, clearWD=FALSE, useWINE=FALSE, WINE=NULL, newWINE=TRUE, WINEPATH=NULL, bugs.seed=1, summary.only=FALSE, save.history=(.Platform$OS.type == "windows" | useWINE==TRUE), over.relax = FALSE)

Arguments

data

either a named list (names corresponding to variable names in the model.file) of the data for the OpenBUGS model, or a vector or list of the names of the data objects used by the model. If data is a one element character vector (such as "data.txt"), it is assumed that data have already been written to the working directory into that file, e.g. by the function bugs.data.

inits

a list with n.chains elements; each element of the list is itself a list of starting

values for the OpenBUGS model, or a function creating (possibly random) initial

values. Alternatively, if inits=NULL, initial values are generated by OpenBUGS. If

inits is a character vector with n.chains elements, it is assumed that inits have

already been written to the working directory into those files, e.g. by the function

bugs.inits.

parameters.to.save

character vector of the names of the parameters to save which should be monitored

model.file

File containing the model written in OpenBUGS code. The extension must be `.txt'. The old convention allowing model.file to be named `.bug' has been eliminated because the new OpenBUGS feature that allows the program image to be saved and later restarted uses the .bug extension for the saved images. Alternatively, model.file can be an R function that contains a BUGS model that is written to a temporary model file (see tempfile) using write.model.

n.chains

number of Markov chains (default: 3)

n.iter

number of total iterations per chain (including burn in; default: 2000)

n.burnin

length of burn in, i.e. number of iterations to discard at the beginning. Default is n.iter/2, that is, discarding the first half of the simulations.

n.thin

Thinning rate. Must be a positive integer. The default is n.thin = 1. The thinning is implemented in the OpenBUGS update phase, so thinned samples are never stored, and they are not counted in n.burnin or n.iter. Setting n.thin=2, doubles the number of iterations OpenBUGS performs, but does not change n.iter or n.burnin. Thinning implemented in this manner is not captured in summaries created by packages such as coda.

bugs

13

saveExec

If TRUE, a re-startable image of the OpenBUGS execution is saved with basename(model.file) and extension .bug in the working directory, which must be specified. The .bug files can be large, so users should monitor them carefully and remove them when not needed.

restart

If TRUE, execution resumes with the final status from the previous execution stored in the .bug file in the working directory. If n.burnin=0,additional iterations are performed and all iterations since the previous burnin are used (including those from past executions). If n.burnin>0, a new burnin is performed, and the previous iterations are discarded, but execution continues from the status at the end of the previous execution. When restart=TRUE, only n.burnin, n.iter, and saveExec inputs should be changed from the call creating the .bug file, otherwise failed or erratic results may be produced. Note the default has n.burnin>0.

debug

if FALSE (default), OpenBUGS is closed automatically when the script has finished running, otherwise OpenBUGS remains open for further investigation. The debug option is not available for linux execution.

DIC

logical; if TRUE (default), compute deviance, pD, and DIC. This is done in Open-

BUGS directly using the rule pD = Dbar - Dhat. If there are less iterations than

required for the adaptive phase, the rule pD=var(deviance) / 2 is used.

digits

number of significant digits used for OpenBUGS input, see formatC

codaPkg

logical; if FALSE (default) a bugs object is returned, if TRUE file names of OpenBUGS output are returned for easy access by the coda package through function read.bugs. A bugs object can be converted to an mcmc.list object as used by the coda package with the method as.mcmc.list (for which a method is provided by R2OpenBUGS).

OpenBUGS.pgm

For Windows or WINE execution, the full path to the OpenBUGS executable. For linux execution, the full path to the OpenBUGS shell script (not required if OpenBUGS is in the user's PATH variable). If NULL (unset) and the environment variable OpenBUGS_PATH is set the latter will be used as the default. If NULL (unset), the environment variable OpenBUGS_PATH is unset and the global option R2OpenBUGS.pgm is not NULL the latter will be used as the default. If nothing of the former is set and OS is Windows, the most recent OpenBUGS version registered in the Windows registry will be used as the default.

working.directory

sets working directory during execution of this function; OpenBUGS' in- and output will be stored in this directory; if NULL, a temporary working directory via tempdir is used.

clearWD

logical; indicating whether the files `data.txt', `inits[1:n.chains].txt', `log.odc', `codaIndex.txt', and `coda[1:nchains].txt' should be removed after OpenBUGS has finished. If set to TRUE, this argument is only respected if codaPkg=FALSE.

useWINE

logical; attempt to use the Wine emulator to run OpenBUGS. Default is FALSE. If WINE is used, the arguments OpenBUGS.pgm and working.directory must be given in form of Linux paths rather than Windows paths (if not NULL).

WINE

Character, path to `wine' binary file, it is tried hard (by a guess and the utilities which and locate) to get the information automatically if not given.

newWINE

Use new versions of Wine that have `winepath' utility

WINEPATH

Character, path to `winepath' binary file, it is tried hard (by a guess and the utilities which and locate) to get the information automatically if not given.

bugs.seed

Random seed for OpenBUGS. Must be an integer between 1-14. Seed specification changed between WinBUGS and OpenBUGS; see the OpenBUGS documentation for details.

summary.only

If TRUE, only a parameter summary for very quick analyses is given, temporary created files are not removed in that case.

save.history If TRUE (the default), trace plots are generated at the end.

over.relax

If TRUE, over-relaxed form of MCMC is used if available from OpenBUGS.

14

bugs

Details To run: 1. Write a BUGS model in an ASCII file (hint: use write.model). 2. Go into R. 3. Prepare the inputs for the bugs function and run it (see Example section). 4. An OpenBUGS window will pop up and R will freeze up. The model will now run in OpenBUGS. It might take awhile. You will see things happening in the Log window within OpenBUGS. When OpenBUGS is done, its window will close and R will work again. 5. If an error message appears, re-run with debug=TRUE. BUGS version support: · OpenBUGS >=3.2.1 Operation system support: · MS Windowsno problem · Linux, intel processorsGUI display and graphics not available. · Mac OS X and Unix in generalpossible with Wine emulation via useWINE=TRUE If useWINE=TRUE is used, all paths (such as working.directory and model.file, must be given in native (Unix) style, but OpenBUGS.pgm can be given in Windows path style (e.g. "c:/Program Files/OpenBUGS/") or native (Unix) style (e.g. "/path/to/wine/folder/dosdevices/c:/Program Files/OpenBUGS/OpenBU

Value

If codaPkg=TRUE the returned values are the names of coda output files written by OpenBUGS containing the Markov Chain Monte Carlo output in the CODA format. This is useful for direct access with read.bugs. If codaPkg=FALSE, the following values are returned:

n.chains n.iter n.burnin n.thin n.keep n.sims sims.array sims.list

see Section `Arguments' see Section `Arguments' see Section `Arguments' see Section `Arguments' number of iterations kept per chain (equal to (n.iter-n.burnin) / n.thin) number of posterior simulations (equal to n.chains * n.keep) 3-way array of simulation output, with dimensions n.keep, n.chains, and length of combined parameter vector list of simulated parameters: for each scalar parameter, a vector of length n.sims for each vector parameter, a 2-way array of simulations, for each matrix parameter, a 3-way array of simulations, etc. (for convenience, the n.keep*n.chains simulations in sims.matrix and sims.list (but NOT sims.array) have been randomly permuted)

sims.matrix

matrix of simulation output, with n.chains*n.keep rows and one column for each element of each saved parameter (for convenience, the n.keep*n.chains simulations in sims.matrix and sims.list (but NOT sims.array) have been randomly permuted)

summary

summary statistics and convergence information for each saved parameter.

mean

a list of the estimated parameter means

sd

a list of the estimated parameter standard deviations

median

a list of the estimated parameter medians

root.short

names of argument parameters.to.save and "deviance"

long.short

indexes; programming stuff

dimension.short dimension of indexes.short

bugs

15

indexes.short last.values pD DIC

indexes of root.short list of simulations from the most recent iteration; they can be used as starting points if you wish to run OpenBUGS for further iterations an estimate of the effective number of parameters, for calculations see the section "Arguments". mean(deviance) + pD

Author(s) Andrew Gelman, [email protected] , http:/www.stat.columbia.edu/~gelman/bugsR/; modifications and packaged by Sibylle Sturtz, [email protected] , Uwe Ligges, and Neal Thomas

References Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B. (2003): Bayesian Data Analysis, 2nd edition, CRC Press. Sturtz, S., Ligges, U., Gelman, A. (2005): R2WinBUGS: A Package for Running WinBUGS from R. Journal of Statistical Software 12(3), 1-16.

See Also print.bugs, plot.bugs, as well as coda and BRugs packages

Examples

# An example model file is given in: model.file <- system.file(package="R2OpenBUGS", "model", "schools.txt") # Let's take a look: file.show(model.file)

# Some example data (see ?schools for details): data(schools) schools

J <- nrow(schools)

y <- schools$estimate

sigma.y <- schools$sd

data <- list ("J", "y", "sigma.y")

inits <- function(){

list(theta=rnorm(J, 0, 100), mu.theta=rnorm(1, 0, 100),

sigma.theta=runif(1, 0, 100))

}

## or alternatively something like:

# inits <- list(

# list(theta=rnorm(J, 0, 90), mu.theta=rnorm(1, 0, 90),

#

sigma.theta=runif(1, 0, 90)),

# list(theta=rnorm(J, 0, 100), mu.theta=rnorm(1, 0, 100),

#

sigma.theta=runif(1, 0, 100))

# list(theta=rnorm(J, 0, 110), mu.theta=rnorm(1, 0, 110),

#

sigma.theta=runif(1, 0, 110)))

parameters <- c("theta", "mu.theta", "sigma.theta")

## Not run: ## You may need to specify "OpenBUGS.pgm"

16 ## also you need write access in the working directory: schools.sim <- bugs(data, inits, parameters, model.file, n.chains=3, n.iter=5000) print(schools.sim) plot(schools.sim) ## End(Not run)

bugs

S Sturtz, U Ligges, A Gelman

doc.uments.com

About Us :: Privacy Policies :: Terms of Service :: Feedback :: Copyright :: Contact Us :: DMCA Policy

Copyright © 2018 doc.uments.com