An Objective Approach to Prior Mass Functions for Discrete Parameter Spaces

Abstract

We present a novel approach to constructing objective prior distributions for discrete parameter spaces. These types of parameter spaces are particularly problematic, as it appears that common objective procedures to design prior distributions are problem specific. We propose an objective criterion, based on loss functions, instead of trying to define objective probabilities directly. We systematically apply this criterion to a series of discrete scenarios, previously considered in the literature, and compare the priors. The proposed approach applies to any discrete parameter space, making it appealing as it does not involve different concepts according to the model. Supplementary materials for this article are available online.

• Binomial
• Hypergeometric
• Kullback–Leibler divergence
• Loss function
• Objective prior.

SUPPLEMENTARY MATERIAL

Proof of Lemmas and Theorems: This file contains the proofs to lemmas and theorems of the main article.

Additional information

Notes on contributors

C. Villa

C. Villa is Lecturer, School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, UK (E-mail: [email protected]). S. G. Walker is Professor, Department of Statistics and Data Sciences, and Division of Statistics and Scientific Computation, University of Texas at Austin, TX 78712 (E-mail: [email protected]).

S. G. Walker

C. Villa is Lecturer, School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, UK (E-mail: [email protected]). S. G. Walker is Professor, Department of Statistics and Data Sciences, and Division of Statistics and Scientific Computation, University of Texas at Austin, TX 78712 (E-mail: [email protected]).