A multidimensional objective prior distribution from a scoring rule

TL;DR

This paper introduces a new objective prior for multidimensional parameters that incorporates dependence structures, overcoming limitations of traditional independent priors, and is proper and model-independent.

Contribution

It extends scoring rule-based objective priors to multidimensional spaces, creating a proper, model-independent prior with dependence structure.

Findings

The proposed prior captures dependence among parameters.

It is proper and does not depend on specific models.

The approach generalizes existing scoring rule methods.

Abstract

The construction of objective priors is, at best, challenging for multidimensional parameter spaces. A common practice is to assume independence and set up the joint prior as the product of marginal distributions obtained via "standard" objective methods, such as Jeffreys or reference priors. However, the assumption of independence a priori is not always reasonable, and whether it can be viewed as strictly objective is still open to discussion. In this paper, by extending a previously proposed objective approach based on scoring rules for the one dimensional case, we propose a novel objective prior for multidimensional parameter spaces which yields a dependence structure. The proposed prior has the appealing property of being proper and does not depend on the chosen model; only on the parameter space considered.