Overall Objective Priors

TL;DR

This paper explores methods for selecting a single objective prior in multi-parameter models to facilitate reasonable posterior inferences across all parameters or functions of interest.

Contribution

It introduces and evaluates three methods for choosing an overall objective prior applicable to multiple parameters or functions.

Findings

The proposed priors perform well across various problems.

Some methods yield priors suitable for all parameters of interest.

The study includes applications to multinomial models.

Abstract

In multi-parameter models, reference priors typically depend on the parameter or quantity of interest, and it is well known that this is necessary to produce objective posterior distributions with optimal properties. There are, however, many situations where one is simultaneously interested in all the parameters of the model or, more realistically, in functions of them that include aspects such as prediction, and it would then be useful to have a single objective prior that could safely be used to produce reasonable posterior inferences for all the quantities of interest. In this paper, we consider three methods for selecting a single objective prior and study, in a variety of problems including the multinomial problem, whether or not the resulting prior is a reasonable overall prior.