Chapter 19: Bayesian Data Analysis

Herbert Hoijtink

Bayesian data analysis It is impossible to give a comprehensive introduction to Bayesian data analysis in just one chapter. In the sequel, I will present what I consider to be the most important components of Bayesian data analysis: parameter estimation based on the Gibbs sampler; the Bayesian counterpart of hypothesis testing (posterior predictive inference); and model selection using the Bayes factor. The chapter will be concluded with a short discussion of Bayesian hierarchical modeling and references to topics that will not be discussed in this chapter. For accessible introductions to Bayesian data analysis the interested reader is referred to Gill (2002) and Lee (1997). Throughout the chapter, references for further reading will be given both to these two books and to more advanced material. It would be easy to fill a whole chapter with a description and discussion of the differences between Bayesian data analysis and the classical frequentist data ...

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