Bayes optimal sequential trial designs

In this paper we look at extensions of this idea. For the null and alternative hypotheses listed above, and under Lerche's sampling cost cθ2, we show that there exists a family of loss functions such that a given boundary, under some restrictions, is Bayes. While the sampling cost is as simple as Lerche's, the loss function is too complicated to be useful. It also has the atypical property of depending on both the stopping time and the value of the Brownian motion upon stopping. Therefore, suboptimal procedures with simple loss/cost structures are also developed.