Applied Bayesian Modelling E-Book

Peter Congdon

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Probability and Statistics
• Sprache: Englisch

Seitenzahl: 887

Veröffentlichungsjahr: 2014

Beschreibung

This book provides an accessible approach to Bayesian computing and data analysis, with an emphasis on the interpretation of real data sets. Following in the tradition of the successful first edition, this book aims to make a wide range of statistical modeling applications accessible using tested code that can be readily adapted to the reader's own applications. The second edition has been thoroughly reworked and updated to take account of advances in the field. A new set of worked examples is included. The novel aspect of the first edition was the coverage of statistical modeling using WinBUGS and OPENBUGS. This feature continues in the new edition along with examples using R to broaden appeal and for completeness of coverage.

Leseprobe

Table of Contents

Cover

Title Page

WILEY SERIES IN PROBABILITY AND STATISTICS

Copyright

Preface

Chapter 1: Bayesian methods and Bayesian estimation

1.1 Introduction

1.2 MCMC techniques: The Metropolis–Hastings algorithm

1.3 Software for MCMC: BUGS, JAGS and R-INLA

1.4 Monitoring MCMC chains and assessing convergence

1.5 Model assessment

References

Chapter 2: Hierarchical models for related units

2.1 Introduction: Smoothing to the hyper population

2.2 Approaches to model assessment: Penalised fit criteria, marginal likelihood and predictive methods

2.3 Ensemble estimates: Poisson–gamma and Beta-binomial hierarchical models

2.4 Hierarchical smoothing methods for continuous data

2.5 Discrete mixtures and dirichlet processes

2.6 General additive and histogram smoothing priors

Exercises

Notes

References

Chapter 3: Regression techniques

3.1 Introduction: Bayesian regression

3.2 Normal linear regression

3.3 Simple generalized linear models: Binomial, binary and Poisson regression

3.4 Augmented data regression

3.5 Predictor subset choice

3.6 Multinomial, nested and ordinal regression

Exercises

Notes

References

Chapter 4: More advanced regression techniques

4.1 Introduction

4.2 Departures from linear model assumptions and robust alternatives

4.3 Regression for overdispersed discrete outcomes

4.4 Link selection

4.5 Discrete mixture regressions for regression and outlier status

4.6 Modelling non-linear regression effects

4.7 Quantile regression

Exercises

Notes

References

Chapter 5: Meta-analysis and multilevel models

5.1 Introduction

5.2 Meta-analysis: Bayesian evidence synthesis

5.3 Multilevel models: Univariate continuous outcomes

5.4 Multilevel discrete responses

5.5 Modelling heteroscedasticity

5.6 Multilevel data on multivariate indices

Exercises

Notes

References

Chapter 6: Models for time series

6.1 Introduction

6.2 Autoregressive and moving average models

6.3 Discrete outcomes

6.4 Dynamic linear and general linear models

6.5 Stochastic variances and stochastic volatility

6.6 Modelling structural shifts

Exercises

Notes

References

Chapter 7: Analysis of panel data

7.1 Introduction

7.2 Hierarchical longitudinal models for metric data

7.3 Normal linear panel models and normal linear growth curves

7.4 Longitudinal discrete data: Binary, categorical and Poisson panel data

7.5 Random effects selection

7.6 Missing data in longitudinal studies

Exercises

Notes

References

Chapter 8: Models for spatial outcomes and geographical association

8.1 Introduction

8.2 Spatial regressions and simultaneous dependence

8.3 Conditional prior models

8.4 Spatial covariation and interpolation in continuous space

8.5 Spatial heterogeneity and spatially varying coefficient priors

8.6 Spatio-temporal models

8.7 Clustering in relation to known centres

Exercises

Notes

References

Chapter 9: Latent variable and structural equation models

9.1 Introduction

9.2 Normal linear structural equation models

9.3 Dynamic factor models, panel data factor models and spatial factor models

9.4 Latent trait and latent class analysis for discrete outcomes

9.5 Latent trait models for multilevel data

9.6 Structural equation models for missing data

Exercises

Notes

References

Chapter 10: Survival and event history models

10.1 Introduction

10.2 Continuous time functions for survival

10.3 Accelerated hazards

10.4 Discrete time approximations

10.5 Accounting for frailty in event history and survival models

10.6 Further applications of frailty models

10.7 Competing risks

Exercises

References

Index

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Guide

Table of Contents

List of Illustrations

Figure 1.1

Figure 2.1

Figure 2.2

Figure 2.3

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6

Figure 6.7

Figure 6.8

Figure 6.9

Figure 8.1

Figure 8.2

Figure 10.1

List of Tables

Table 2.1

Table 2.2

Table 2.3

Table 2.4

Table 2.5

Table 3.1

Table 3.2

Table 3.3

Table 3.4

Table 4.1

Table 4.2

Table 6.1

Table 6.2

Table 7.1

Table 7.2

Table 9.1

Table 9.2

Table 9.3

Table 9.4

Table 9.5

Table 9.6

Table 10.1

Table 10.2

Applied Bayesian Modelling

Second Edition

Peter Congdon

Centre for Statistics and Department of Geography, Queen Mary, University of London, UK

WILEY SERIES IN PROBABILITY AND STATISTICS

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

519.5′42– dc23

2014004862

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

ISBN: 978-1-119-95151-3

Preface

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 [email protected].

Peter Congdon, London

Chapter 1Bayesian methods and Bayesian estimation

1.1 Introduction

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

1.1

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.

Such techniques play a major role in applications such as spatial disease patterns, small domain estimation for survey outcomes (Ghosh and Rao, 1994), meta-analysis across several studies (Sutton and Abrams, 2001), educational and psychological testing (Sahu, 2002; Shiffrin et al., 2008) and performance comparisons (e.g. Racz and Sedransk, 2010; Ding et al., 2013).