Artin Armagan

Posterior consistency in linear models under shrinkage priors

We investigate the asymptotic behaviour of posterior distributions of regression coefficients in high-dimensional linear models as the number of dimensions grows with the number of observations. We show that the posterior distribution concentrates in neighbourhoods of the true parameter under simple sufficient conditions. These conditions hold under popular shrinkage priors given some sparsity assumptions. Copyright 2013, Oxford University Press.

A note on mean-field variational approximations in Bayesian probit models

We correct some conclusions presented by Consonni and Marin (2007) on the performance of mean-field variational approximations to Bayesian inferences in the case of a simple probit model. We show that some of their presentations are misleading and thus their results do not fairly present the performance of such approximations in terms of point estimation under the specified model.