Combining Evidence
Statistics Theory
2022-02-08 v1 Statistics Theory
Abstract
The problem of combining the evidence concerning an unknown, contained in each of Bayesian inference bases, is discussed. This can be considered as a generalization of the problem of pooling 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.
Keywords
Cite
@article{arxiv.2202.02922,
title = {Combining Evidence},
author = {Michael Evans and Yang Jian Guo},
journal= {arXiv preprint arXiv:2202.02922},
year = {2022}
}