ing beta ... 200 valid values Abstracting alpha ... 200 valid values Abstracting sigma ... 200 valid values Reading Data file... Abstracting beta ... 200 valid values Abstracting alpha ... 200 valid values Abstracting sigma ... 200 valid values 10 Next, you will be prompted to specify which (if any) variables take values restricted to either the range (0, 1) or to the positive real line. CODA requires this information in order to correctly compute Gelman and Rubin (1992)'s convergence diagnostic for non-normal variables (see x4.2), and to produce kernel density estimates within the appropriate range (see x3.1). Are any variables restricted to values between 0 and 1 (y/n) ? 1: For the line example, you should respond n to this question. The next prompt to appear is as follows: Are any variables restricted to all positive values (y/n) ? 1: For the line example, you should respond y to this question, which causes the following display to appear: Available variables: +---------------+--...

e wrong, which is even worse. Please let us know of any successes or failures. Beware - Gibbs sampling can be dangerous!. BUGS c flcopyright MRC Biostatistics Unit 1995. ALL RIGHTS RESERVED. The support of the Economic and Social Research Council (UK) is gratefully acknowledged. The work was funded in part by ESRC (UK) Award Number H519 25 5023. 1 2 Contents 1 Introduction 5 1.1 What is BUGS? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 For what kind of problems is BUGS best suited? . . . . . . . . . . . . . . . . . . . . . 5 1.3 Markov Chain Monte Carlo (MCMC) techniques . . . . . . . . . . . . . . . . . . . . 5 1.4 A simple example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Hardware platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.6 Software . . .

Richardson and Green (1997) present a method of performing a Bayesian analysis of data from a finite mixture distribution with an unknown number of components. Their method is a Markov Chain Monte Carlo (MCMC) approach, which makes use of the "reversible jump" methodology described by Green (1995). We describe an alternative MCMC method which views the parameters of the model as a (marked) point process, extending methods suggested by Ripley (1977) to create a Markov birth-death process with an appropriate stationary distribution. Our method is easy to implement, even in the case of data in more than one dimension, and we illustrate it on both univariate and bivariate data. Keywords: Bayesian analysis, Birth-death process, Markov process, MCMC, Mixture model, Model Choice, Reversible Jump, Spatial point process 1 Introduction Finite mixture models are typically used to model data where each observation is assumed to have arisen from one of k groups, each group being suitably modelle...

Maps of regional morbidity and mortality rates are useful tools in determining spatial patterns of disease. Combined with socio-demographic census information, they also permit assessment of environmental justice, i.e., whether certain subgroups suffer disproportionately from certain diseases or other adverse effects of harmful environmental exposures. Bayes and empirical Bayes methods have proven useful in smoothing crude maps of disease risk, eliminating the instability of estimates in low-population areas while maintaining geographic resolution. In this paper we extend existing hierarchical spatial models to account for temporal effects and spatio-temporal interactions. Fitting the resulting highly-parametrized models requires careful implementation of Markov chain Monte Carlo (MCMC) methods, as well as novel techniques for model evaluation and selection. We illustrate our approach using a dataset of county-specific lung cancer rates in the state of Ohio during the period 1968--1988...

In this paper we study the ergodicity properties of some adaptive Monte Carlo Markov chain algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated from the output of a so-called adaptive MCMC sampler converge to the required value and can even, under more stringent assumptions, satisfy a central limit theorem. We prove that the conditions required are satisfied for the Independent Metropolis-Hastings algorithm and the Random Walk Metropolis algorithm with symmetric increments. Finally we propose an application of these results to the case where the proposal distribution of the Metropolis-Hastings update is a mixture of distributions from a curved exponential family.

A new approach to Markov chain Monte Carlo simulation was recently proposed by Propp and Wilson. This approach, unlike traditional ones, yields samples which have exactly the desired distribution. The Propp-Wilson algorithm requires this distribution to have a certain structure called monotonicity. In this paper an idea of Kendall is applied to show how the algorithm can be extended to the case where monotonicity is replaced by anti-monotonicity. As illustrating examples, simulations of the hard-core model and the random-cluster model are presented.

This paper analyzes the Gibbs sampler applied to a standard variance component model, and considers the question of how many iterations are required for convergence. It is proved that for K location parameters, with J observations each, the number of iterations required for convergence (for large K and J) is a constant times

This research examines the ability of six popular Web search engines, individually and collectively, tolocateWeb pages containing common marketing/management phrases. We propose and validate a model for search engine performance that is able to represent key patterns of coverage and overlap among the engines. The model enables us to estimate the typical additional benefit of using multiple search engines - depending on the particular set of engines being considered. It also provides an estimate of the number of relevantWeb pages not found byanyofthe engines. For a typical marketing/management phrase we estimate that the "best" search engine locates about 50% of the pages, and all six engines together find about 90% of the total. The model is also used to examine how properties of aWeb page and characteristics of a phrase affect the probabilitythatagiven searchenginewillfindagiven page. For example, we find that the number of Web page links increases the prospect that each of...

We describe a general approach using Bayesian analysis for the estimation of parameters in physiological pharmacokinetic models. The chief statistical difficulty in estimation with these models is that any physiological model that is even approximately realistic will have a large number of parameters, often comparable to the number of observations in a typical pharmacokinetic experiment (for example, 28 measurements and 15 parameters for each subject). In addition, the parameters are generally poorly identified, akin to the well-known ill-conditioned problem of estimating a mixture of declining exponentials. Our modeling includes (1) hierarchical population modeling as in Wakefield (1994), which allows partial pooling of information among different experimental subjects; (2) a pharmacokinetic model including compartments for well-perfused tissues, poorly-perfused tissues, fat, and the liver; and (3) informative prior distributions for population parameters, which is possible be- Sch...

This paper integrates and extends some recent computational advances in Bayesian inference with the objective of more fully realizing the Bayesian promise of coherent inference and model comparison in economics. It combines Markov chain Monte Carlo and independence Monte Carlo with importance sampling to provide an efficient and generic method for updating posterior distributions. It exploits the multiplicative decomposition of marginalized likelihood into predictive factors, to compute posterior odds ratios efficiently and with minimal further investment in software. It argues for the use of predictive odds ratios in model comparison in economics. Finally, it suggests procedures for public reporting that will enable remote clients to conveniently modify priors, form posterior expectations of their own functions of interest, and update the posterior distribution with new observations. A series of examples explores the practicality and efficiency of these methods.