Sequential testing problems for Poisson processes. (English) Zbl 1081.62546

Summary: 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 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.


62L10 Sequential statistical analysis
62C10 Bayesian problems; characterization of Bayes procedures
62M02 Markov processes: hypothesis testing
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