Statistical Assessment of Replicability via Bayesian Model Criticism

Assessment of replicability is critical to ensure the quality and rigor of scientific research. In this paper, we discuss inference and modeling principles for replicability assessment. Targeting distinct application scenarios, we propose two types of Bayesian model criticism approaches to identify potentially irreproducible results in scientific experiments. They are motivated by established Bayesian prior and posterior predictive model-checking procedures and generalize many existing replicability assessment methods. Finally, we discuss the statistical properties of the proposed replicability assessment approaches and illustrate their usages by simulations and examples of real data analysis, including the data from the Reproducibility Project: Psychology and a systematic review of impacts of pre-existing cardiovascular disease on COVID-19 outcomes.