Why optional stopping is a problem for Bayesians

Recently, optional stopping has been a subject of debate in the Bayesian psychology community. Rouder (2014) argues that optional stopping is no problem for Bayesians, and even recommends the use of optional stopping in practice, as do Wagenmakers et al. (2012). This article addresses the question whether optional stopping is problematic for Bayesian methods, and specifies under which circumstances it is or is not. By slightly varying and extending Rouder's (2014) experiment, we show that resilience to optional stopping breaks down in some cases which, we argue, a pragmatic Bayesian cannot ignore. We emphasize the difference between the purely subjective and an objective Bayesian viewpoint, and their implications for optional stopping. We conclude that optional stopping is a problem for Bayesian inference with a composite null hypothesis with the (partly) objective Bayesian methods that are used in practice.