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Alternative Approaches and Noise Benefits in Hypothesis-Testing Problems in the Presence of Partial Information = = Kismi̇ Bi̇lgi̇ Bulunan Hi̇potez Sinama Problemleri̇nde Alternati̇f Yaklasimlar ve Gurultu Kazanimlari.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Alternative Approaches and Noise Benefits in Hypothesis-Testing Problems in the Presence of Partial Information =/
Reminder of title:	Kismi̇ Bi̇lgi̇ Bulunan Hi̇potez Sinama Problemleri̇nde Alternati̇f Yaklasimlar ve Gurultu Kazanimlari.
remainder title:	Kismi̇ Bi̇lgi̇ Bulunan Hi̇potez Sinama Problemleri̇nde Alternati̇f Yaklasimlar ve Gurultu Kazanimlari.
Author:	Bayram, Suat.
Description:	1 online resource (184 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 83-10, Section: B.
Contained By:	Dissertations Abstracts International83-10B.
Subject:	Probability. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29047598click for full text (PQDT)
ISBN:	9798209968870

Alternative Approaches and Noise Benefits in Hypothesis-Testing Problems in the Presence of Partial Information = = Kismi̇ Bi̇lgi̇ Bulunan Hi̇potez Sinama Problemleri̇nde Alternati̇f Yaklasimlar ve Gurultu Kazanimlari.
Bayram, Suat.

Alternative Approaches and Noise Benefits in Hypothesis-Testing Problems in the Presence of Partial Information =Kismi̇ Bi̇lgi̇ Bulunan Hi̇potez Sinama Problemleri̇nde Alternati̇f Yaklasimlar ve Gurultu Kazanimlari.Kismi̇ Bi̇lgi̇ Bulunan Hi̇potez Sinama Problemleri̇nde Alternati̇f Yaklasimlar ve Gurultu Kazanimlari. - 1 online resource (184 pages)

Source: Dissertations Abstracts International, Volume: 83-10, Section: B.

Thesis (Ph.D.)--Bilkent Universitesi (Turkey), 2011.

Includes bibliographical references

Performance 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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798209968870Subjects--Topical Terms:

518898
Probability.
Index Terms--Genre/Form:

542853
Electronic books.

Alternative Approaches and Noise Benefits in Hypothesis-Testing Problems in the Presence of Partial Information = = Kismi̇ Bi̇lgi̇ Bulunan Hi̇potez Sinama Problemleri̇nde Alternati̇f Yaklasimlar ve Gurultu Kazanimlari.
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245 1 0 $a Alternative Approaches and Noise Benefits in Hypothesis-Testing Problems in the Presence of Partial Information = $b Kismi̇ Bi̇lgi̇ Bulunan Hi̇potez Sinama Problemleri̇nde Alternati̇f Yaklasimlar ve Gurultu Kazanimlari.
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500 $a Source: Dissertations Abstracts International, Volume: 83-10, Section: B.
500 $a Advisor: Gezici, Sinan.
502 $a Thesis (Ph.D.)--Bilkent Universitesi (Turkey), 2011.
504 $a Includes bibliographical references
520 $a Performance 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.
520 $a Optimal olmayan bazi sezicilerin performansi, gozlemlerine bagimsiz gurultu eklenerek artirilabilir. Tezin ilk kisminda ek gurultunun etkileri, Bayes ve minimaks kriterlerinin genellestirilmesini saglayan kisiti Bayes kriterine gore calisilmaktadir. Genel M'li bilesik hipotez sinamalari baz alinarak, ek gurultunun optimal olasilik dagilim fonksiyonu incelenmektedir. Ayni zamanda, sezicinin performansinin gurultu eklenerek gelistirilip gelistirilemeyecegiyle ilgili yeter kosullar turetilmektedir. Bunlara ek olarak, basit hipotez sinama problem- leri daha ayrintili olarak calisilmakta ve basit hipotezlere ozel ek yeter kosullar elde edilmektedir. Ayrica, belli kosullar altinda, bir basit M'li hipotez sinama problemindeki optimal ek gurultunun olasilik yogunluk fonksiyonunun, en fazla M farkli deger arasinda rasgelelestirme icerdigi gosterilmektedir. Daha sonra, op- timal gurultu dagilimini elde etmek icin global optimizasyon, analitik ve disbukey gevsetme yaklasimlari ele alinmaktadir. Son olarak, kuramsal sonuclari incele- mek icin sezim ornekleri sunulmaktadir.Tezin ikinci kisminda, kismi onsel bilgi bulunan bilesik M'li hipotez sinama problemleri icin ek gurultunun etkileri calisilmaktadir. Optimal ek gurultu, bilinmeyen onsel olasiliklar icin birbicimli dagilim (kriter 1) veya en az uy- gun dagilim (kriter 2) varsayan iki kritere gore elde edilmektedir. Her bir kriter icin optimal gurultunun istatistiksel ozellikleri elkde edilmektedir. Ozel olarak, optimal gurultinun kriter l'e gore sabit bir sinyal seviyesiyle ya da kriter 2'ye gore sonlu sayidaki sinyal seviyesinin rasgelelestirilmesiyle ifade edilebilecegi gosterilmektedir. Bunlara ek olarak, bazi bilesik hipotezler altindaki parametre dagilimlarinin bilinmedigi durumlar ele alinmakta ve risklerin uzerine ust sinirlar elde edilmektedir. Son olarak, kuramsal sonuclari gostermek icin bir sezim ornegi sunulmaktadir.Tezin ucuncu kisminda, ek gurultunun ikili bilesik hipotez sinama problem- leri uzerindeki etkileri calisilmaktadir. Bir Neyman-Pearson (NP) cercevesi ele alinmakta ve en yuksek yanlis alarm olasiligi uzerindeki simirlama altinda sezim performansinin en yuksek seviyeye cikarilmasina calisilmaktadir. Sezim perfor- mansi, alternatif hipotez altindaki muhtemel parametre degerlerine karsilik gelen sezim olasiliklarinin toplami, minimumu ve maksimumu cinsinden hesaplanmak- tadir. Her bir durum icin sezim performansinin gelistirilip gelistirilemeyecegiyle ilgili yeter kosullar turetilmektedir. Ayni zamanda, optimal ek gurultunun is- tatistiksel ozellikleri sunulmakta ve ortaya cikan yanlis alarm olasiliklari ve sezim performansi uzerindeki sinirlar incelenmektedir. Bunlara ilave olarak, optimal ek gurultunun olasilik dagilimini elde etmek icin optimizasyon kurami tabanli yaklasimlar tartisilmaktadir. Son olarak, kuramsal sonuclari incelemek icin bir sezim ornegi sunulmaktadir.Son olarak, alternatif hipotez altindaki onsel olasilik dagiliminda belir- sizlik bulunan bilesik hipotez sinama problemleri icin kisitli NP yaklasimi calisilmaktadir. Kisitli NP karar kurali, en kotu durumdaki sezim ve yanlis alarm olasiliklari uzerindeki kisitlamalar altinda, ortalama sezim olasiligini en yuksek seviyeye cikarmayi hedefler ve en kotu durumdaki sezim olasiligi uzerindeki kisitlama seviyesini, onsel olasilik dagilimindaki belirsizligin mik- tarina gore ayarlar. Kisitli NP kriterine gore optimal karar kurallari incelen- mekte ve optimal kisitli NP karar kuralinin hesaplanmasi icin bir algoritma saglanmaktadir. Bunlara ek olarak, ortalama sezim olasiliginin, minimum sezim olasigi uzerindeki kisitlama seviyesinin kesin azalan ve icbukey bir fonksiyonu oldugu gozlenmektedir. Son olarak, bir sezim ornegi sunulmakta ve daha genel senaryolara genisletimler tartisilmaktadir.
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