Posterior consistency in linear models under shrinkage priors

Abstract

We investigate the asymptotic behavior 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 neighborhoods of the true parameter under simple sufficient conditions. These conditions hold under popular shrinkage priors given some sparsity assumptions.

To appear in Biometrika

References in corpus (4)

• Variational Relevance Vector Machines
• Generalized Beta Mixtures of Gaussians
• Bernstein von Mises Theorems for Gaussian Regression with increasing number of regressors
• Bayesian variable selection for high dimensional generalized linear models: convergence rates of the fitted densities

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