Bayesian Evidence Synthesis for the common effect model

Bayes Factors, the Bayesian tool for hypothesis testing, are receiving increasing attention in the literature. Compared to their frequentist rivals ($p$-values or test statistics), Bayes Factors have the conceptual advantage of providing evidence both for and against a null hypothesis, and they can be calibrated so that they do not depend so heavily on the sample size. Research on the synthesis of Bayes Factors arising from individual studies has received increasing attention, mostly for the fixed effects model for meta-analysis. In this work, we review and propose methods for combining Bayes Factors from multiple studies, depending on the level of information available, focusing on the common effect model. In the process, we provide insights with respect to the interplay between frequentist and Bayesian evidence. We assess the performance of the methods discussed via a simulation study and apply the methods in an example from the field of positive psychology.