Visualization in Bayesian Data Analysis

Abstract

Modern Bayesian inference is highly computational but commonly pro- ceeds without reference to modern developments in statistical graphics. This should change. Visualization has two important roles to play in Bayesian data analysis: (1) For model checking, graphs of data or functions of data and estimated model (for example, residual plots) can be visually compared to corresponding graphs of replicated data sets. This is the fully-model-based version of exploratory data analysis. The goal is to use graphical tools to explore aspects of the data not captured by the fitted model. (2) For model understanding, graphs of inferences can be used to summarize estimates and uncertainties about batches of parameters in hierarchical and other structured models. Traditional tools of summarizing models (such as looking at coef- ficients and analytical relationships) are too crude to usefully summarize the multiple levels of variation and uncertainty that arise in Bayesian hierarchical models.