Approximate Bayesian Predictive Distributions and Model Selection

Abstract

An observation is assumed to arise from one of k models that may depend on parameters. A prior distribution is specified by assigning probabilities to each of the models and by assigning probability densities to the parameters of each model. If an approximate prior distribution is used, the predictive distribution of a future observation will be approximate. Bounds on the error in the predictive distribution are derived from bounds on the error in the prior distribution. A method for selecting a vague prior distribution for the parameters of each of the k models is given.

Key Words:

• Approximate predictive distribution
• Stable measurement
• Vague prior distribution