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| List of Figures | |
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| List of Tables | |
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| Preface | |
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| Acknowledgments | |
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| Acronyms | |
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| Introduction to Bayesian inference | |
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| Introduction: Bayesian modeling in the 21st century | |
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| Definition of statistical models | |
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| Bayes theorem | |
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| Model based Bayesian inference | |
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| Inference using conjugate prior distributions | |
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| Non Conjugate Analysis | |
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| Problems | |
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| Markov Chain Monte Carlo Algorithms in Bayesian Inference | |
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| Simulation, Monte Carlo integration and their implementation in Bayesian inference | |
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| Markov chain Monte Carlo methods | |
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| Popular MCMC algorithms | |
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| Summary and closing remarks | |
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| Problems | |
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| The WinBUGS software: Introduction, Set-up and Basic Analysis | |
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| Introduction and historical background | |
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| The WinBUGS environment | |
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| Preliminaries on using WinBUGS | |
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| Building Bayesian models in WinBUGS | |
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| Compiling the model and simulating values | |
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| Basic Output analysis using the Sample Monitor Tool | |
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| Summarizing the procedure | |
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| Chapter summary and concluding comments | |
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| Problems | |
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| The WinBUGS Software: Illustration, Results and Further Analysis | |
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| A complete example of running MCMC in WinBUGS for a simple model | |
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| Further output analysis using the inference menu | |
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| Multiple chains | |
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| Changing the properties of a figure | |
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| Other tools and menus | |
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| Summary and concluding remarks | |
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| Problems | |
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| Introduction to Bayesian models: Normal models | |
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| General modeling principles | |
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| Model specification in Normal regression models | |
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| Using vectors and multivariate priors in normal regression models | |
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| Analysis of variance models | |
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| Problems | |
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| Incorporating categorical variables in normal models&further modeling issues | |
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| Dummy variables and design matrices | |
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| Analysis of variance models using dummy variables | |
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| Analysis of covariance models | |
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| A Bioassay example | |
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| Further modeling issues | |
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| Closing remarks | |
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| Problems | |
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| Introduction to generalized linear models: Binomial and Poisson data | |
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| Introduction | |
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| Prior distributions | |
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| Posterior inference | |
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| Poisson regression models | |
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| Binomial Regression Models | |
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| Models for contingency tables | |
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| Problems | |
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| Generalized linear models: Models for positive continuous data, count data and other GLM based extensions | |
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| Models with non-standard distributions | |
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| Models for positive continuous response variables | |
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| Additional models for count data | |
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| Further GLM based models and extensions | |
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| Problems | |
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| Bayesian Hierarchical models | |
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| Introduction | |
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| Some simple examples | |
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| The generalized linear mixed model formulation | |
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| Discussion, closing remarks and further reading | |
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| Problems | |
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| The predictive distribution and model checking | |
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| Introduction | |
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| Estimating the predictive distribution for future or missing observations using MCMC | |
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| Using the predictive distribution for model checking | |
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| Using cross-validation predictive densities for model checking, evaluation and comparison | |
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| Illustration of a complete predictive analysis: Normal regression models | |
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| Discussion | |
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| Problems | |
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| Bayesian Model and Variable Evaluation | |
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| Prior predictive distributions as measures of model comparison: Posterior model odds and Bayes Factors | |
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| Sensitivity of the posterior model probabilities: The Bartlett-Lindley paradox | |
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| Computation of the marginal likelihood | |
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| Computation of the marginal likelihood using WinBUGS | |
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| Bayesian variable selec | |