A BAYESIAN TEST OF SOME CLASSICAL HYPOTHESES- WITH APPLICATIONS TO SEQUENTIAL CLINICAL TRIALS

Abstract Consider someone who sets out to collect data sequentially in such a way as to disprove a hypothesis, H 0, about the value of θ, the mean of a normal distribution. Observation is continued as long as the posterior probability of H 0 exceeds α1 and stopped when it falls below it. It is shown that if a non-zero prior probability, p, is assigned to H 0(0≤α1 < p) and the remaining prior probability is spread over alternate values of θ that the probability that H 0 will eventually be rejected when true is With non-zero assignment of p it is therefore not possible to sample to a foregone conclusion. The Wald 3-decision scheme is shown to be equivalent to setting and assigning prior probability of to the alternatives θ = θ0 + Δ and θ = θ0 − Δ. Anomalous features of this scheme, particularly for the case of unknown σ, are shown to be a consequence of the unrealistic nature of the alternatives assumed. It is suggested that meaningful assignments of p are possible in practice by considering the minimum num...