Simultaneous Bayesian-frequentist sequential testing of nested hypotheses

Conditional frequentist tests of a precise hypothesis versus a composite al ternative have recently been developed, and have been shown to be equivalen t to conventional Bayes tests in the very strong sense that the reported fr equentist error probabilities equal the posterior probabilities of the hypo theses. These results are herein extended to sequential testing, and yield fully frequentist sequential tests that are considerably-easier to use than are conventional sequential tests. Among the interesting properties of the se new tests is the lack of dependence of the reported error probabilities on the stopping rule, seeming to lend frequentist support to the stopping r ule principle.