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August 1998 Bayesian goodness-of-fit testing using infinite-dimensional exponential families
Isabella Verdinelli, Larry Wasserman
Ann. Statist. 26(4): 1215-1241 (August 1998). DOI: 10.1214/aos/1024691240


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.


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Isabella Verdinelli. Larry Wasserman. "Bayesian goodness-of-fit testing using infinite-dimensional exponential families." Ann. Statist. 26 (4) 1215 - 1241, August 1998.


Published: August 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0930.62027
MathSciNet: MR1647645
Digital Object Identifier: 10.1214/aos/1024691240

Primary: 62F15, 62G10

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.26 • No. 4 • August 1998
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