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dc.contributor.advisorGezici, Sinan
dc.contributor.authorBayram, Suat
dc.date.accessioned2016-01-08T18:16:01Z
dc.date.available2016-01-08T18:16:01Z
dc.date.issued2011
dc.identifier.urihttp://hdl.handle.net/11693/15280
dc.descriptionAnkara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 2011.en_US
dc.descriptionThesis (Ph. D.) -- Bilkent University, 2011.en_US
dc.descriptionIncludes bibliographical references leaves 153-164.en_US
dc.description.abstractPerformance of some suboptimal detectors can be enhanced by adding independent noise to their observations. In the first part of the dissertation, the effects of additive noise are studied according to the restricted Bayes criterion, which provides a generalization of the Bayes and minimax criteria. Based on a generic M-ary composite hypothesis-testing formulation, the optimal probability distribution of additive noise is investigated. Also, sufficient conditions under which the performance of a detector can or cannot be improved via additive noise are derived. In addition, simple hypothesis-testing problems are studied in more detail, and additional improvability conditions that are specific to simple hypotheses are obtained. Furthermore, the optimal probability distribution of the additive noise is shown to include at most M mass points in a simple M-ary hypothesis-testing problem under certain conditions. Then, global optimization, analytical and convex relaxation approaches are considered to obtain the optimal noise distribution. Finally, detection examples are presented to investigate the theoretical results. In the second part of the dissertation, the effects of additive noise are studied for M-ary composite hypothesis-testing problems in the presence of partial prior information. Optimal additive noise is obtained according to two criteria, which assume a uniform distribution (Criterion 1) or the least-favorable distribution (Criterion 2) for the unknown priors. The statistical characterization of the optimal noise is obtained for each criterion. Specifically, it is shown that the optimal noise can be represented by a constant signal level or by a randomization of a finite number of signal levels according to Criterion 1 and Criterion 2, respectively. In addition, the cases of unknown parameter distributions under some composite hypotheses are considered, and upper bounds on the risks are obtained. Finally, a detection example is provided to illustrate the theoretical results. In the third part of the dissertation, the effects of additive noise are studied for binary composite hypothesis-testing problems. A Neyman-Pearson (NP) framework is considered, and the maximization of detection performance under a constraint on the maximum probability of false-alarm is studied. The detection performance is quantified in terms of the sum, the minimum and the maximum of the detection probabilities corresponding to possible parameter values under the alternative hypothesis. Sufficient conditions under which detection performance can or cannot be improved are derived for each case. Also, statistical characterization of optimal additive noise is provided, and the resulting false-alarm probabilities and bounds on detection performance are investigated. In addition, optimization theoretic approaches for obtaining the probability distribution of optimal additive noise are discussed. Finally, a detection example is presented to investigate the theoretical results. Finally, the restricted NP approach is studied for composite hypothesistesting problems in the presence of uncertainty in the prior probability distribution under the alternative hypothesis. A restricted NP decision rule aims to maximize the average detection probability under the constraints on the worstcase detection and false-alarm probabilities, and adjusts the constraint on the worst-case detection probability according to the amount of uncertainty in the prior probability distribution. Optimal decision rules according to the restricted NP criterion are investigated, and an algorithm is provided to calculate the optimal restricted NP decision rule. In addition, it is observed that the average detection probability is a strictly decreasing and concave function of the constraint on the minimum detection probability. Finally, a detection example is presented, and extensions to more generic scenarios are discussed.en_US
dc.description.statementofresponsibilityBayram, Suaten_US
dc.format.extentxiii, 164 leavesen_US
dc.language.isoEnglishen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectHypothesis-testingen_US
dc.subjectNoise Enhanced Detectionen_US
dc.subjectRestricted Bayesen_US
dc.subjectStochastic Resonanceen_US
dc.subjectComposite Hypothesesen_US
dc.subjectBayes Risken_US
dc.subjectNeyman-Pearsonen_US
dc.subjectMaxminen_US
dc.subjectLeast-favorable Prioren_US
dc.subject.lccTK5102.9 .B391 2011en_US
dc.subject.lcshSignal detection.en_US
dc.subject.lcshSignal processing.en_US
dc.subject.lcshStochastic processes.en_US
dc.subject.lcshElectronic noise.en_US
dc.subject.lcshNoise--Mathematical models.en_US
dc.subject.lcshStatistical hypothesis testing.en_US
dc.titleAlternative approaches and noise benefits in hypothesis-testing problems in the presence of partial informationen_US
dc.typeThesisen_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.publisherBilkent Universityen_US
dc.description.degreePh.D.en_US
dc.identifier.itemidB129723


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