An Objective Prior from a Scoring Rule |
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Authors: | Stephen G Walker Cristiano Villa |
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Institution: | 1.Department of Mathematics, University of Texas at Austin, 2515 Speedway, Austin, TX 78712, USA;2.School of Mathematics, Statistics & Physics, University of Newcastle, Newcastle upon Tyne NE1 7RU, UK |
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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. Although in itself this provides motivation for an objective prior, the prior also minimizes a corresponding information criterion. |
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Keywords: | Bregman divergence convex function Euler– Lagrange equation objective prior |
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