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| Preface | |
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| Principles of Bayesian Inference | |
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| Bayesian updating | |
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| MCMC techniques | |
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| The basis for MCMC | |
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| MCMC sampling algorithms | |
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| MCMC convergence | |
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| Competing models | |
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| Setting priors | |
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| The normal linear model and generalized linear models | |
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| Data augmentation | |
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| Identifiability | |
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| Robustness and sensitivity | |
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| Chapter themes | |
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| References | |
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| Model Comparison and Choice | |
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| Introduction: formal methods, predictive methods and penalized deviance criteria | |
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| Formal Bayes model choice | |
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| Marginal likelihood and Bayes factor approximations | |
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| Predictive model choice and checking | |
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| Posterior predictive checks | |
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| Out-of-sample cross-validation | |
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| Penalized deviances from a Bayes perspective | |
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| Multimodel perspectives via parallel sampling | |
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| Model probability estimates from parallel sampling | |
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| Worked example | |
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| References | |
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| Regression for Metric Outcomes | |
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| Introduction: priors for the linear regression model | |
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| Regression model choice and averaging based on predictor selection | |
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| Robust regression methods: models for outliers | |
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| Robust regression methods: models for skewness and heteroscedasticity | |
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| Robustness via discrete mixture models | |
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| Non-linear regression effects via splines and other basis functions | |
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| Dynamic linear models and their application in non-parametric regression | |
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| Exercises | |
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| References | |
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| Models for Binary and Count Outcomes | |
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| Introduction: discrete model likelihoods vs. data augmentation | |
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| Estimation by data augmentation: the Albert-Chib method | |
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| Model assessment: outlier detection and model checks | |
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| Predictor selection in binary and count regression | |
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| Contingency tables | |
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| Semi-parametric and general additive models for binomial and count responses | |
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| Exercises | |
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| References | |
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| Further Questions in Binomial and Count Regression | |
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| Generalizing the Poisson and binomial: overdispersion and robustness | |
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| Continuous mixture models | |
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| Discrete mixtures | |
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| Hurdle and zero-inflated models | |
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| Modelling the link function | |
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| Multivariate outcomes | |
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| Exercises | |
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| References | |
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| Random Effect and Latent Variable Models for Multicategory Outcomes | |
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| Multicategory data: level of observation and relations between categories | |
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| Multinomial models for individual data: modelling choices | |
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| Multinomial models for aggregated data: modelling contingency tables | |
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| The multinomial probit | |
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| Non-linear predictor effects | |
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| Heterogeneity via the mixed logit | |
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| Aggregate multicategory data: the multinomial-Dirichlet model and extensions | |
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| Multinomial extra variation | |
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| Latent class analysis | |
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| Exercises | |
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| References | |
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| Ordinal Regression | |
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| Aspects and assumptions of ordinal data models | |
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| Latent scale and data augmentation | |
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| Assessing model assumptions: non-parametric ordinal regression and assessing ordinality | |
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| Location-scale ordinal regression | |
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| Structural interpretations with aggregated ordinal data | |
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| Log-linear models for contingency tables with ordered categories | |
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| Multivariate ordered outcomes | |
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| Exercises | |
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| References | |
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| Discrete Spatial Data | |
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| Introduction | |
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| Univariate responses: the mixed ICAR model and extensions | |
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| Spatial robustness | |
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| Multivariate spatial priors | |
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| Varying predictor effect models | |
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| Exercises | |
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| References | |
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| Time Series Models for Discrete Variables | |
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| Introduction: time dependence in observations and latent data | |
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| Observation-driven dependence | |
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| Parameter-driven dependenc | |