Harmonic Bayesian prediction under alpha-divergence
arXiv:1605.05899
Abstract
We investigate Bayesian shrinkage methods for constructing predictive distributions. We consider the multivariate Normal model with a known covariance matrix and show that the Bayesian predictive density with respect to Stein's harmonic prior dominates the best invariant Bayesian predictive density, when the dimension is greater than three. Alpha-divergence from the true distribution to a predictive distribution is adopted as a loss function.
28 pages, major revision, 1: The minimaxity proof is added. 2: The heat equation is no longer necessary