An Objective Prior from a Scoring Rule

TL;DR

This paper introduces a new objective prior distribution based on scoring rules and divergence measures, connecting information theory with Bayesian prior selection.

Contribution

It proposes a novel objective prior derived from convex functions and Bregman divergence, linking scoring rules with prior determination.

Findings

The prior is obtained by setting the score function to a constant.

The proposed prior minimizes a specific information criterion.

Provides a natural connection between scoring rules and objective Bayesian priors.

Abstract

In this paper we introduce a novel objective prior distribution levering on the connections between information, divergence and scoring rules. In particular, we do so from the starting point of convex functions representing information in density functions. This provides a natural route to proper local scoring rules using Bregman divergence. Specifically, we determine the prior which solves setting the score function to be a constant. While in itself this provides motivation for an objective prior, the prior also minimizes a corresponding information criterion.