Statistica Sinica 10(2000), 715-729

SEQUENTIAL DETECTION OF SIGNALS WITH KNOWN

SHAPE AND UNKNOWN MAGNITUDE

M. Beibel

Albert-Ludwigs-Universität Freiburg

Abstract: We study a problem of sequential detection in a continuous time change-point model with a transition period. Let denote a Brownian motion process which has zero drift during the time interval and drift during the time interval . Here is a known deterministic function and and are unknown parameters. The goal is to find a stopping time of that stops as soon and as reliably as possible after the change-point . We consider stopping rules based on mixtures of likelihoods and show that they are approximately Bayes optimal.

Key words and phrases: Bayes problem, change-point, sequential detection, transition period.