Necessary and sufficient conditions for bounded stopping time of sequential bayes tests in one parameter exponential families1

Abstract

The problem of sequently testing one-sided hypotheses about the parameter in a one-parameter exponential family, continuous with respect to Lebesgue measure, is consiered in a Bayesian framework. The paper gives a simple necessary and sufficient condition for the Bayes sampling rule to be bounded. The risk fucntion is taken to be a constant times the number of observations plus a weighted probability of error. The sufficient condition for boundness is generalized to other risk functions as wells.