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Applied Bayesian Modelling, 2nd Edition

Book Description

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.

Table of Contents

  1. Cover
  2. Title Page
  3. WILEY SERIES IN PROBABILITY AND STATISTICS
  4. Copyright
  5. Preface
  6. Chapter 1: Bayesian methods and Bayesian estimation
    1. 1.1 Introduction
    2. 1.2 MCMC techniques: The Metropolis–Hastings algorithm
    3. 1.3 Software for MCMC: BUGS, JAGS and R-INLA
    4. 1.4 Monitoring MCMC chains and assessing convergence
    5. 1.5 Model assessment
    6. References
  7. Chapter 2: Hierarchical models for related units
    1. 2.1 Introduction: Smoothing to the hyper population
    2. 2.2 Approaches to model assessment: Penalised fit criteria, marginal likelihood and predictive methods
    3. 2.3 Ensemble estimates: Poisson–gamma and Beta-binomial hierarchical models
    4. 2.4 Hierarchical smoothing methods for continuous data
    5. 2.5 Discrete mixtures and dirichlet processes
    6. 2.6 General additive and histogram smoothing priors
    7. Exercises
    8. Notes
    9. References
  8. Chapter 3: Regression techniques
    1. 3.1 Introduction: Bayesian regression
    2. 3.2 Normal linear regression
    3. 3.3 Simple generalized linear models: Binomial, binary and Poisson regression
    4. 3.4 Augmented data regression
    5. 3.5 Predictor subset choice
    6. 3.6 Multinomial, nested and ordinal regression
    7. Exercises
    8. Notes
    9. References
  9. Chapter 4: More advanced regression techniques
    1. 4.1 Introduction
    2. 4.2 Departures from linear model assumptions and robust alternatives
    3. 4.3 Regression for overdispersed discrete outcomes
    4. 4.4 Link selection
    5. 4.5 Discrete mixture regressions for regression and outlier status
    6. 4.6 Modelling non-linear regression effects
    7. 4.7 Quantile regression
    8. Exercises
    9. Notes
    10. References
  10. Chapter 5: Meta-analysis and multilevel models
    1. 5.1 Introduction
    2. 5.2 Meta-analysis: Bayesian evidence synthesis
    3. 5.3 Multilevel models: Univariate continuous outcomes
    4. 5.4 Multilevel discrete responses
    5. 5.5 Modelling heteroscedasticity
    6. 5.6 Multilevel data on multivariate indices
    7. Exercises
    8. Notes
    9. References
  11. Chapter 6: Models for time series
    1. 6.1 Introduction
    2. 6.2 Autoregressive and moving average models
    3. 6.3 Discrete outcomes
    4. 6.4 Dynamic linear and general linear models
    5. 6.5 Stochastic variances and stochastic volatility
    6. 6.6 Modelling structural shifts
    7. Exercises
    8. Notes
    9. References
  12. Chapter 7: Analysis of panel data
    1. 7.1 Introduction
    2. 7.2 Hierarchical longitudinal models for metric data
    3. 7.3 Normal linear panel models and normal linear growth curves
    4. 7.4 Longitudinal discrete data: Binary, categorical and Poisson panel data
    5. 7.5 Random effects selection
    6. 7.6 Missing data in longitudinal studies
    7. Exercises
    8. Notes
    9. References
  13. Chapter 8: Models for spatial outcomes and geographical association
    1. 8.1 Introduction
    2. 8.2 Spatial regressions and simultaneous dependence
    3. 8.3 Conditional prior models
    4. 8.4 Spatial covariation and interpolation in continuous space
    5. 8.5 Spatial heterogeneity and spatially varying coefficient priors
    6. 8.6 Spatio-temporal models
    7. 8.7 Clustering in relation to known centres
    8. Exercises
    9. Notes
    10. References
  14. Chapter 9: Latent variable and structural equation models
    1. 9.1 Introduction
    2. 9.2 Normal linear structural equation models
    3. 9.3 Dynamic factor models, panel data factor models and spatial factor models
    4. 9.4 Latent trait and latent class analysis for discrete outcomes
    5. 9.5 Latent trait models for multilevel data
    6. 9.6 Structural equation models for missing data
    7. Exercises
    8. Notes
    9. References
  15. Chapter 10: Survival and event history models
    1. 10.1 Introduction
    2. 10.2 Continuous time functions for survival
    3. 10.3 Accelerated hazards
    4. 10.4 Discrete time approximations
    5. 10.5 Accounting for frailty in event history and survival models
    6. 10.6 Further applications of frailty models
    7. 10.7 Competing risks
    8. Exercises
    9. References
  16. Index
  17. WILEY SERIES IN PROBABILITY AND STATISTICS
  18. End User License Agreement