Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
Abstract : We consider a Bayesian approach to goodness of fit, that is, to the problem of testing whether or not a given parametric model is compatible with the data at hand. We thus consider a parametric family F, parametrised by a parameter t. The null hypothesis is then that the true distribution f is in F, that is, that a cdf transform of the observation gives a uniform rv. The alternative hypothesis is thus that all transforms give non-uniform rv's on [0,1]. Instead of using a functional basis as in Verdinelli and Wasserman (1998), we represent the distribution under the alternative as a mixture of beta distributions. Estimation within both parametric and nonparametric structures are implemented using MCMC algorithms that estimate the number of components in the mixture. Since we are concerned with a goodness of fit problem, it is more of interest to consider a functional distance to the tested model as the basis of our test, rather than the corresponding Bayes factor, since the later puts more emphasis on the parameters. We therefore propose a new test procedure based on the expected distance, with both an asymptotic justification and a finite sampler implementation.
ROBERT Christian P., ROUSSEAU Judith
Université de PARIS - DAUPHINE
Place du Maréchal de Lattre De Tassigny - 75775 PARIS CEDEX 16 - FRANCE
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