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Multisource Bayesian sequential binary hypothesis testing problem

Dayanık, Savaş and Sezer, Semih Onur (2012) Multisource Bayesian sequential binary hypothesis testing problem. Annals of Operations Research, 201 (1). pp. 99-130. ISSN 0254-5330 (Print) 1572-9338 (Online)

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Official URL: http://dx.doi.org/10.1007/s10479-012-1217-z

Abstract

We consider the problem of testing two simple hypotheses about unknown local characteristics of several independent Brownian motions and compound Poisson processes. All of the processes may be observed simultaneously as long as desired before a fi nal choice between hypotheses is made. The objective is to find a decision rule that identifi es the correct hypothesis and strikes the optimal balance between the expected costs of sampling and choosing the wrong hypothesis. Previous work on Bayesian sequential hypothesis testing in continuous time provides a solution when the characteristics of these processes are tested separately. However, the decision of an observer can improve greatly if multiple information sources are available both in the form of continuously changing signals (Brownian motions) and marked count data (compound Poisson processes). In this paper, we combine and extend those previous efforts by considering the problem in its multisource setting. We identify a Bayes optimal rule by solving an optimal stopping problem for the likelihood ratio process. Here, the likelihood ratio process is a jump-diffusion, and the solution of the optimal stopping problem admits a two-sided stopping region. Therefore, instead of using the variational arguments (and smooth-fit principles) directly, we solve the problem by patching the solutions of a sequence of optimal stopping problems for the pure diffusion part of the likelihood ratio process. We also provide a numerical algorithm and illustrate it on several examples.

Item Type:Article
Uncontrolled Keywords:Bayesian sequential identification, Jump-diffusion processes, Optimal stopping
Subjects:Q Science > QA Mathematics > QA273-280 Probabilities. Mathematical statistics
ID Code:21036
Deposited By:Semih Onur Sezer
Deposited On:27 Nov 2012 12:28
Last Modified:02 Jul 2013 15:17

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