Optimal sequentially planned tests under side conditions

Abstract

From classical decision theory it is well known that Bayes-optimal procedures can, on the one hand, be very important for individual/private decisions and, on the other hand, be of interest for deriving structural properties of „reasonable” procedures. But due to the (at least partial) arbitrariness in determining the prior distribution, these procedures are not accepted by administrations and public health offices. Here requirements concerning the error probabilities (p-values), side conditions concerning the consumer’s or producer’s risk, restrictions on the total sample size, the sampling costs, the number of stages etc. are of importance. This means that the class of „admissible” decision procedures is restricted by (external) side conditions.