A Bayesian way to make stopping rules matter

Disputes between advocates of Bayesians and more orthodox approaches to statistical inference presuppose that Bayesians must regard stopping rules, which play an important role in orthodox statistical methods, as evidentially irrelevant. In this essay, I show that this is not the case and that the stopping rule is evidentially relevant given some Bayesian confirmation measures that have been seriously proposed. However, I show that accepting a confirmation measure of this sort comes at the cost of rejecting two useful ancillary Bayesian principles.