Part II: Fundamentals of Bayesian Data Analysis

For most problems of applied Bayesian statistics, the data analyst must go beyond the simple structure of prior distribution, likelihood, and posterior distribution. In Chapter 6, we discuss methods of assessing the sensitivity of posterior inferences to model assumptions and checking the fit of a probability model to data and substantive information. Model checking allows an escape from the tautological aspect of formal approaches to Bayesian inference, under which all conclusions are conditional on the truth of the posited model. Chapter 7 considers evaluating and comparing models using predictive accuracy, adjusting for the parameters being fit to the data. Chapter 8 outlines the role of study design and methods of data collection in probability modeling, focusing on how to set up Bayesian inference for sample surveys, designed experiments, and observational studies; this chapter contains some of the most conceptually distinctive and potentially difficult material in the book. Chapter 9 discusses the use of Bayesian inference in applied decision analysis, illustrating with examples from social science, medicine, and public health. These four chapters explore the creative choices that are required, first to set up a Bayesian model in a complex problem, then to perform the model checking and confidence building that is typically necessary to make posterior inferences scientifically defensible, and finally to use the inferences in decision making.