Bayesian evidence synthesis for informative hypotheses: An introduction

To establish a theory one needs cleverly designed and well-executed studies with appropriate and correctly interpreted statistical analyses. Equally important, one also needs replications of such studies and a way to combine the results of several replications into an accumulated state of knowledge. An approach that provides an appropriate and powerful analysis for studies targeting prespecified theories is the use of Bayesian informative hypothesis testing. An additional advantage of the use of this Bayesian approach is that combining the results from multiple studies is straightforward. In this article, we discuss the behavior of Bayes factors in the context of evaluating informative hypotheses with multiple studies. By using simple models and (partly) analytical solutions, we introduce and evaluate Bayesian evidence synthesis (BES) and compare its results to Bayesian sequential updating. By doing so, we clarify how different replications or updating questions can be evaluated. In addition, we illustrate BES with two simulations, in which multiple studies are generated to resemble conceptual replications. The studies in these simulations are too heterogeneous to be aggregated with conventional research synthesis methods.