An Objective Prior from a Scoring Rule

Entropy

Stephen G. Walker¹  Cristiano Villa² 

[1] Department of Mathematics, University of Texas at Austin, 2515 Speedway, Austin, TX 78712, USA;School of Mathematics, Statistics & Physics, University of Newcastle, Newcastle upon Tyne NE1 7RU, UK;

关键词: Bregman divergence;    convex function;    Euler–Lagrange equation;    objective prior;   

DOI  :  10.3390/e23070833

来源: DOAJ

【 摘 要 】

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. Although in itself this provides motivation for an objective prior, the prior also minimizes a corresponding information criterion.

【 授权许可】

Unknown