This thesis investigates variable stage size multistage hypothesis testing in three different contexts, each building on the previous. We first consider the problem of sampling a random process in stages until it crosses a predetermined boundary at the end of a stage – first for Brownian motion and later for a sum of i.i.d. random variables. A multistage sampling procedure is derived and its properties are shown to be not only sufficient but also necessary for asymptotic optimality as the… CONTINUE READING