Optimal Prior Pooling from Expert Opinions

TL;DR

This paper introduces a novel method for pooling expert opinions into a single prior using a minimization of information principle in the square-root density space, enabling exact calculations for exponential family distributions.

Contribution

It proposes a new approach to prior pooling based on extrinsic means in the Hilbert sphere, applicable to exponential families and contaminated priors.

Findings

Optimal prior is identified as an extrinsic mean in the sphere.

Exact calculations are possible for exponential family distributions.

Method can handle contaminated priors near a base prior.

Abstract

The pooling of prior opinions is an important area of research and has been for a number of decades. The idea is to obtain a single belief probability distribution from a set of expert opinion belief distributions. The paper proposes a new way to provide a resultant prior opinion based on a minimization of information principle. This is done in the square-root density space, which is identified with the positive orthant of Hilbert unit sphere of differentiable functions. It can be shown that the optimal prior is easily identified as an extrinsic mean in the sphere. For distributions belonging to the exponential family, the necessary calculations are exact, and so can be directly applied. The idea can also be adopted for any neighbourhood of a chosen base prior and spanned by a finite set of ``contaminating" directions.