Spatial nonparametric Bayesian models

Abstract

Introduction and Motivation The prior distribution is an essential ingredient of any Bayesian analysis, and it plays a major role in determining the final results. As such, Bayesians attempt to use prior distributions that have certain properties. Perhaps the main property is a desire to accurately reflect prior information, i.e., information external to the experiment at hand. We would supplement this vague property with a second equally vague property. The posterior distribution should exhibit behavior that is qualitatively acceptable. The second property for prior distributions is vague, but carries with it several implications. An immediate implication is that we should dispense with parametric Bayesian models in all but the simplest of settings! This perhaps surprising implication follows from an examination of various cases. As a case in point, consider a survival analysis setting where there is a follow-up period of limited duration. With large samples, one could hope