Exploratory data analysis and model criticism with posterior plots

The use of techniques of exploratory data analysis and model criticism represent important stages in many statistical investigations. One of the attractive features of a Bayesian analysis is that it can lend itself well to graphical summary. To produce this graphical summary it is generally necessary to restrict attention to a small number of key parameters. The graphical approach described can be adopted whenever an appropriate likelihood function can be specified. Solutions to some of the principal computational problems associated with implementing a graphical Bayesian analysis based on posterior plots are presented. Nuisance parameters are handled in two ways: by incorporating them directly into the computation of exact posterior distributions; and by integrating them out of a conditional analysis at an early stage when the former approach is infeasible. The latter proposal facilitates the handling of higher dimensional nuisance parameter vectors. Examples taken from the areas of time series and microeconomics are presented to illustrate the efficacy of the approach.