On a property of a non–local moment prior

Abstract

The paper provides objective motivation for the class of non–local moment prior, introduced for the purposes of Bayesian hypothesis testing using Bayes factors. The motivation is that it minimizes Fisher information among a large class of density. Being a minimizer of some measure of information is an important feature so that the test, even within a Bayesian framework, has an objective criterion.

Keywords:

• Bayesian hypothesis test
• calculus of variations
• convex function
• Euler–Lagrange equation
• Fisher information

MSC:

• 62C10; 62F15

Acknowledgments

The author is grateful for the comments and suggestions of a reviewer.