Combining Evidence

TL;DR

This paper explores methods for combining evidence from multiple Bayesian inference bases, highlighting the effectiveness of linear opinion pooling in maintaining consensus and discussing the role of Jeffrey conditionalization.

Contribution

It demonstrates that linear opinion pooling is the most suitable method for combining evidence while preserving consensus and discusses its properties in Bayesian evidence synthesis.

Findings

Linear opinion pool preserves consensus in evidence combination.

Linear pooling does not preserve prior independence but remains appropriate.

Jeffrey conditionalization is key in combining evidence.

Abstract

The problem of combining the evidence concerning an unknown, contained in each of $k$ Bayesian inference bases, is discussed. This can be considered as a generalization of the problem of pooling $k$ priors to determine a consensus prior. The linear opinion pool of Stone (1961) is seen to have the most appropriate properties for this role. In particular, linear pooling preserves a consensus with respect to the evidence and other rules do not. While linear pooling does not preserve prior independence, it is shown that it still behaves appropriately with respect to the expression of evidence in such a context. For the general problem of combining evidence, Jeffrey conditionalization plays a key role.