Evans Michael
Department of Statistical Sciences, University of Toronto, Toronto, ON M5G 1Z5, Canada.
Entropy (Basel). 2025 Jun 18;27(6):654. doi: 10.3390/e27060654.
The problem of combining statistical evidence concerning an unknown, contained in each of the Bayesian inference bases, is discussed. This can be considered as being related to the problem of pooling priors to determine a consensus prior, but the focus here is instead on combining a measure of statistical evidence to obtain a consensus measure of statistical evidence. The linear opinion pool 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 statistical evidence in such a context. For the more general problem of combining statistical evidence, where the priors as well as the sampling models may differ, Jeffrey conditionalization plays a key role.
讨论了在每个贝叶斯推理基础中关于未知量的统计证据组合问题。这可以被认为与合并先验以确定共识先验的问题相关，但这里的重点是合并统计证据的度量以获得统计证据的共识度量。线性意见池被认为在此角色中具有最合适的属性。特别是，线性合并在证据方面保持了共识，而其他规则则不然。虽然线性合并不保持先验独立性，但结果表明，在这种情况下，它在统计证据的表达方面仍表现得当。对于更一般的统计证据组合问题，其中先验以及抽样模型可能不同，杰弗里条件化起着关键作用。
