Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

BAYESIAN GOODNESS OF FIT TESTING USING INFINITE DIMENSIONAL EXPONENTIAL FAMILIES

Publication Date

January, 1996

Publication Type

Tech Report

Author(s)

Isabella Verdinelli and Larry Wasserman

Abstract

We develop a nonparametric Bayes factor for testing the fit of a parametric model. We begin with a nominal parametric family which we then embed into an infinite dimensional exponential family. The new model then has a parametric and nonparametric component. We give the log density of the nonparametric component a Gaussian process prior. An asymptotic consistency requirement puts a restriction on the form of the prior leaving us with a single hyperparameter for which we suggest a default value based on simulation experience. Then we construct a Bayes factor to test the nominal model versus the semiparametric alternative. Finally, we show that the Bayes factor is consistent. The proof of the consistency is based on approximating the model by a sequence of exponential families.

Areas of Research