Bayesian Modeling Using WinBugs: An Introduction

Abstract

Since the mid- 1980s, the development of widely accessible powerful computers and the implementation of Markov chain Monte Carlo (MCMC) methods have led to an explosion of interest in Bayesian statistics and modeling. This was followed by an extensive research for new Bayesian methodologies generating the practical application of complicated models used over a wide range of sciences. During the late 199Os, BUGS emerged in the foreground. BUGS was a free software that could fit complicated models in a relatively easy manner, using standard MCMC methods. Since 1998 or so, WinBUGS, the Windows version of BUGS, has earned great popularity among researchers of diverse scientific fields. Therefore, an increased need for an introductory book related to Bayesian models and their implementation via WinBUGS has been realized. The objective of the present book is to offer an introduction to the principles of Bayesian modeling, with emphasis on model building and model implementation using WinBUGS. Detailed examples are provided, ranging from very simple to more advanced and realistic ones. Generalized linear models (GLMs), which are familiar to most students and researchers, are discussed. Details concerning model building, prior specification, writing the WinBUGS code and the analysis and interpretation of the WinBUGS output are also provided. Because of the introductory character of the book, I focused on elementary models, starting from the normal regression models and moving to generalized linear models. Even more advanced readers, familiar with such models, may benefit from the Bayesian implementation using WinBUGS. Basic knowledge of probability theory and statistics is assumed. Computations that could not be performed in WinBUGS are illustrated using R. Therefore, a minimum knowledge of R is also required. This manuscript can be used as the main textbook in a second-level course of Bayesian statistics focusing on modeling and/or computation. Alternatively, it can serve as a companion (to a main textbook) in an introductory course of a Bayesian statistics. Finally, because of its structure, postgraduate students and other researchers can complete a self-taught tutorial course on Bayesian modeling by following the material of this book. All datasets and code used in the book are available in the book’s Webpage: www. stat-athens.aueb.gr/”jbn/winbugs-book. IOANNIS NTZOUFRA