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Schwaferts, Patrick (10. February 2021): Updating Consistency in Bayes Factors. Department of Statistics: Technical Reports, No.236


When it comes to extracting information from data by means of Bayes rule, it should not matter if all available data are considered at once or if Bayesian updating is performed subsequently with partitions of the data. This property is called updating consistency. However, in the context of Bayes factors, a prominent Bayesian tool that is used for comparing hypotheses, some researchers illustrated that updating consistency might not be given. Therefore, this technical report addresses the updating consistency of Bayes factors and shows its existence. In that, it serves as mathematical basis for the evaluation of the origin of putative updating inconsistencies. In addition, results about updating mixture priors are brought into the terminology commonly employed in the context of Bayes factors, as these were used in the elaboration about updating consistency. The depicted results imply that a necessary condition for updating consistency is to consider and report not only the Bayes factor value alone but also the posterior distributions as outcome of the analysis.