Congdon Peter - Applied Bayesian Modelling

Established by WALTER A. SHEWHART and SAMUEL S. WILKS

Editors: David J. Balding, Noel A. C. Cressie, Garrett M. Fitzmaurice,

Geof H. Givens, Harvey Goldstein, Geert Molenberghs, David W. Scott,Adrian F. M. Smith, Ruey S. Tsay, Sanford Weisberg

Editors Emeriti: J. Stuart Hunter, Iain M. Johnstone, Joseph B. Kadane,Jozef L. Teugels

A complete list of the titles in this series appears at the end of this volume.

This edition first published 2014

2014 John Wiley & Sons, Ltd

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Library of Congress Cataloging-in-Publication Data

Congdon, P.

Applied Bayesian modelling / Peter Congdon. Second edition.

pages cm

Includes bibliographical references and index.

ISBN 978-1-119-95151-3 (cloth)

1. Bayesian statistical decision theory. 2. Mathematical statistics. I. Title.

QA279.5.C649 2014

519.542 dc23

2014004862

A catalogue record for this book is available from the British Library.

ISBN: 978-1-119-95151-3

My gratitude is due to Wiley for proposing a revised edition of Applied Bayesian Modelling, first published in 2003. Much has changed since then for those seeking to apply Bayesian principles or to exploit the growing advantages of Bayesian estimation.

The central program used throughout the text in worked examples is BUGS, though R packages such as R-INLA, R2BayesX and MCMCpack are also demonstrated. Reference throughout the text to BUGS can be taken to refer both to WinBUGS and the ongoing OpenBUGS program, on which future development will concentrate (see http://www.openbugs.info/w/). There is a good deal of continuity between the final WinBUGS14 version and OpenBUGS (for details of differences see http://www.openbugs.info/w.cgi/OpenVsWin), though OpenBUGS has a wider range of sampling choices, distributions and functions. BUGS code can also be simply adapted to JAGS applications and the JAGS interfaces with R such as rjags.

Although R interfaces to BUGS or encapsulating the program are now widely used, the BUGS programming language itself remains a central aspect. Direct experience in WinBUGS or OpenBUGS programming is important as a preliminary to using R Interfaces such as BRUGS and rjags.

For learning Bayesian methods, especially if the main goal is data analysis per se, BUGS has advantages both practical and pedagogical. It can be seen as a half-way house between menu driven Bayesian computing (still not really established in any major computing package, though SAS has growing Bayesian capabilities) on the one hand, and full development of independent code, including sampling algorithms, on the other.

Many thanks are due to the following for comments on chapters or programming advice: Sid Chib, Cathy Chen, Brajendra Sutradhar and Thomas Kneib.

Please send comments or questions to me at .

Peter Congdon, London

Bayesian analysis of data in the health, social and physical sciences has been greatly facilitated in the last two decades by improved scope for estimation via iterative sampling methods. Recent overviews are provided by Brooks et al. (2011), Hamelryck et al. (2012), and Damien et al. (2013). Since the first edition of this book in 2003, the major changes in Bayesian technology relevant to practical data analysis have arguably been in distinct new approaches to estimation, such as the INLA method, and in a much extended range of computer packages, especially in R, for applying Bayesian techniques (e.g. Martin and Quinn, 2006; Albert, 2007; Statisticat LLC, 2013).

Among the benefits of the Bayesian approach and of sampling methods of Bayesian estimation (Gelfand and Smith, 1990; Geyer, 2011) are a more natural interpretation of parameter uncertainty (e.g. through credible intervals) (Lu et al., 2012), and the ease with which the full parameter density (possibly skew or multi-modal) may be estimated. By contrast, frequentist estimates may rely on normality approximations based on large sample asymptotics (Bayarri and Berger, 2004). Unlike classical techniques, the Bayesian method allows model comparison across non-nested alternatives, and recent sampling estimation developments have facilitated new methods of model choice (e.g. Barbieri and Berger, 2004; Chib and Jeliazkov, 2005). The flexibility of Bayesian sampling estimation extends to derived structural parameters combining model parameters and possibly data, and with substantive meaning in application areas, which under classical methods might require the delta technique. For example, Parent and Rivot (2012) refer to management parameters derived from hierarchical ecological models.

New estimation methods also assist in the application of hierarchical models to represent latent process variables, which act to borrow strength in estimation across related units and outcomes (Wikle, 2003; Clark and Gelfand, 2006). Letting and denote joint and conditional densities respectively, the paradigm for a hierarchical model specifies

based on an assumption that observations are imperfect realisations of an underlying process and that units are exchangeable. Usually the observations are considered conditionally independent given the process and parameters.