The Annals of Statistics

Bayesian goodness-of-fit testing using infinite-dimensional exponential families

Isabella Verdinelli and Larry Wasserman

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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.

Article information

Ann. Statist., Volume 26, Number 4 (1998), 1215-1241.

First available in Project Euclid: 21 June 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F15 62G10

Bayes factor consistency Gaussian process prior Markov chain Monte Carlo nonparametric Bayesian inference sieve


Verdinelli, Isabella; Wasserman, Larry. Bayesian goodness-of-fit testing using infinite-dimensional exponential families. Ann. Statist. 26 (1998), no. 4, 1215--1241. doi:10.1214/aos/1024691240.

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