Stopping rules matter to Bayesians too

This paper considers a key point of contention between classical and Bayesian statistics—the issue of stopping rules, or more generally, outcome spaces, and their influence on statistical analysis. Firstly, a working definition of classical and Bayesian statistical tests is given, which makes clear that i) once a test has been conducted and an outcome recorded, only the classical approach to inference depends on the full outcome space for the test, and ii) full outcome spaces are nevertheless relevant to both the classical and Bayesian approaches, when it comes to planning/choosing a test. The latter commonality between the approaches undermines at least one argument against classical statistics. But it also undermines what may have been a compelling argument against the Bayesian approach—the Bayesian indifference to persistent experimenters and their optional stopping rules. Indeed, the final section of the paper offers three Bayesian error theories for the pro-classical ‘optional stopping intuition’.