Title

Consistent Bayesian model selection in p<=n settings

Abstract

Let Y n = (y1, . . . , yn)′ denote a random vector, X n an n × p matrix of real numbers, and p a p × 1 regression vector. This article addresses the selection of non-zero components of p when it is assumed that Y n  N(X n p, 2I n) and p  n. Model selection is based on the calculation of posterior model probabilities using non-local prior densities on the regression coefficients for each possible model. The non-local prior densities used for model definition are obtained as products of normal moment priors and are called pMOM prior densities. Under mild conditions on the matrix (X′nXn)−1, we demonstrate that the use of these priors guarantees that the posterior probability of the true model converges to 1 as the sample size increases, and that the resulting model selection procedure exhibits an “oracle” property in the p  n setting.

Disciplines

Clinical Trials



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