Multisource Bayesian sequential binary hypothesis testing problem
 Savas Dayanik,
 Semih O. Sezer
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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 final choice between hypotheses is made. The objective is to find a decision rule that identifies 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 likelihoodratio process. Here, the likelihoodratio process is a jumpdiffusion, and the solution of the optimal stopping problem admits a twosided stopping region. Therefore, instead of using the variational arguments (and smoothfit principles) directly, we solve the problem by patching the solutions of a sequence of optimal stopping problems for the pure diffusion part of the likelihoodratio process. We also provide a numerical algorithm and illustrate it on several examples.
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 Title
 Multisource Bayesian sequential binary hypothesis testing problem
 Journal

Annals of Operations Research
Volume 201, Issue 1 , pp 99130
 Cover Date
 20121201
 DOI
 10.1007/s104790121217z
 Print ISSN
 02545330
 Online ISSN
 15729338
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Bayesian sequential identification
 Jumpdiffusion processes
 Optimal stopping
 Industry Sectors
 Authors

 Savas Dayanik ^{(1)}
 Semih O. Sezer ^{(2)}
 Author Affiliations

 1. Departments of Industrial Engineering and Mathematics, Bilkent University, Bilkent, 06800, Ankara, Turkey
 2. Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla, 34956, Istanbul, Turkey