Bayesian sequential testing with expectation constraints

We study a stopping problem arising from a sequential testing of two simple hypotheses H0 and H1 on the drift rate of a Brownian motion. We impose an expectation constraint on the stopping rules allowed and show that an optimal stopping rule satisfying the constraint can be found among the rules of the following type: stop if the posterior probability for H1 attains a given lower or upper barrier; or stop if the posterior probability comes back to a fixed intermediate point after a sufficiently large excursion. Stopping at the intermediate point means that the testing is abandoned without accepting H0 or H1. In contrast to the unconstrained case, optimal stopping rules, in general, cannot be found among interval exit times. Thus, optimal stopping rules in the constrained case qualitatively differ from optimal rules in the unconstrained case.

Optimal stopping rules for exponential data

A problem of sequential sampling from an Exponential Distribution is considered in this research. The problem is formulated in the stochastic dynamicprogramming framework and the objective is to determine a control policy maximizing the total expected reward. It is assumed that under standardassumptions the control limit policy is optimal. Two types of optimal stopping problems are considered. First one is the problem of sampling withoutrecall that once the decision maker cannot return to that observation at a later time, the second type of optimal stopping problems is sampling with recallwhere the decision maker can select any observation which he has taken earlier.