  A/B testing is one of the most successful applications of statistical theory
in modern Internet age. One problem of Null Hypothesis Statistical Testing
(NHST), the backbone of A/B testing methodology, is that experimenters are not
allowed to continuously monitor the result and make decision 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 an 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 with continuous monitoring when proper
stopping rules are used, and illustrate the theoretical results with concrete
simulation illustrations. We point out common bad practices where stopping
rules are not proper and also compare our methodology to NHST corrections.
General guidelines for researchers and practitioners are also provided.
