Continuous sequential decision in the presence of a finite number of hypotheses

Abstract

Given a finite probability space <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</tex> and an a priori distribution <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P = P(0) = \{p_{i}(0)\}</tex> , exact expressions for minimum search time (to determine the one and only one nonzero mean process) are derived. Only one point <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</tex> may be observed at a given time, in contrast to the more standard decision theory problem where all n processes are observed simultaneously. The problem is formulated in continuous time, as a limiting case of discrete-time hypothesis tests. The performance of the optimal strategy is shown to be far superior to the performance of some standard strategies.