Continuous Monitoring of A/B Tests without Pain: Optional Stopping in Bayesian Testing

A/B testing is one of the most successful applications of statistical theory in the Internet age. A crucial problem of Null Hypothesis Statistical Testing (NHST), the backbone of A/B testing methodology, is that experimenters are not allowed to continuously monitor the results and make decisions in real time. Many people see this restriction as a setback against the trend in the technology toward real time data analytics. Recently, Bayesian Hypothesis Testing, which intuitively is more suitable for real time decision making, attracted growing interest as a viable alternative to NHST. While corrections of NHST for the continuous monitoring setting are well established in the existing literature and known in A/B testing community, the debate over the issue of whether continuous monitoring is a proper practice in Bayesian testing exists among both academic researchers and general practitioners. In this paper, we formally prove the validity of Bayesian testing under proper stopping rules, and illustrate the theoretical results with concrete simulation illustrations. We point out common bad practices where stopping rules are not proper, and discuss how priors can be learned objectively. General guidelines for researchers and practitioners are also provided.