Harmonic Bayesian prediction under alpha-divergence

TL;DR

This paper explores Bayesian predictive methods under alpha-divergence loss, demonstrating that harmonic priors outperform invariant priors in multivariate Normal models when dimensions exceed three.

Contribution

It introduces a dominance result for harmonic Bayesian predictive densities over invariant ones under alpha-divergence loss in high-dimensional Normal models.

Findings

Harmonic Bayesian predictive density dominates invariant predictive density for dimension > 3.

Results are established under alpha-divergence loss.

The study advances understanding of Bayesian prediction in multivariate Normal models.

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.