Sequential testing problems for Poisson processes
The Annals of Statistics · 2000 · Volume 28 · Issue 3
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 continuous fit. A rigorous proof of the optimality of the Wald’s sequential probability ratio test in the variational formulation of the problem is obtained as a consequence of the solution of the Bayesian problem.
Keywords
34K10, 60G40, 60J75, 62C10, 62L10, 62L15, Bayes decision rule, free-boundary differential-difference Stephan problem, Itô's formula, measure of jumps and its compensator, Optimal stopping, point (counting)(Cox) process, Poisson process, principles of continuous and smooth fit, sequential testing, SPRT (sequential probability ratio test)
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