A multidimensional objective prior distribution from a scoring rule

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 standardobjective 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.

Automated summary

Constructing objective priors for multidimensional parameter spaces is challenging, and a common approach assumes independence and uses standard objective methods to obtain marginal distributions. In this paper, a novel objective prior is proposed by extending the objective method for one-dimensional case, allowing for a dependence structure in multidimensional parameter spaces.