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On a Class of Objective Prior from Scoring Rules

Leisen, Fabrizio, Villa, Cristiano, Walker, Stephen G. (2019) On a Class of Objective Prior from Scoring Rules. Bayesian Analysis, . ISSN 1936-0975. (In press) (doi:10.1214/19-BA1187) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided)

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Abstract

Objective prior distributions represent an important tool that allows one to have the advantages of using a Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off the chosen statistical model and in the majority of cases the resulting prior is improper, which can pose limitations to a practical implementation, even when the complexity of the model is moderate. In this paper we propose to take a novel look at the construction of objective prior distributions, where the connection with a chosen sampling distribution model is removed. We explore the notion of defining objective prior distributions which allow one to have some degree of flexibility, in particular in exhibiting some desirable features, such as being proper, or log-concave, convex etc. The basic tool we use are proper scoring rules and the main result is a class of objective prior distributions that can be employed in scenarios where the usual model based priors fail, such as mixture models and model selection via Bayes factors. In addition, we show that the proposed class of priors is the result of minimising the information it contains, providing solid interpretation to the method.

Item Type: Article
DOI/Identification number: 10.1214/19-BA1187
Uncontrolled keywords: calculus of variation; differential entropy; Euler-Lagrange equation; Fisher information; invariance; objective Bayes; proper scoring rules
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Cristiano Villa
Date Deposited: 26 Oct 2019 13:20 UTC
Last Modified: 06 Feb 2020 10:03 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/77889 (The current URI for this page, for reference purposes)
Leisen, Fabrizio: https://orcid.org/0000-0002-2460-6176
Villa, Cristiano: https://orcid.org/0000-0002-2670-2954
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