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MaPhySto
Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1998-29
November 1998




Solution of the Bayesian Sequential Testing Problem for a Poisson Process

by:

Goran Peskir

Albert N. Shiryaev

Abstract

We present the explicit solution of the Bayesian problem of sequential testing of two simple hypotheses about the intensity of an observed Poisson process. The method of proof consists of reducing the initial problem to a free-boundary differential-difference Stephan problem, and solving the latter by use of the principles of smooth and continous fit. The principle of continous fit emerges as some unexpected novelty; in this context playing the key role. The rigorous proof of the optimality of the Wald sequential probability ratio test in the variational formulation of the same sequential problem is obtained as an immediate consequence.

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This paper has now been published in Expanded version appears under the title "Sequential testing problems for Poisson processes" in Ann. Statist. 28, 837-859 (2000)