928 research outputs found
Noise enhanced hypothesis-testing according to restricted Neyman-Pearson criterion
Cataloged from PDF version of article.Noise enhanced hypothesis-testing is studied according to the restricted Neyman-Pearson (NP) criterion. First, a problem formulation is presented for obtaining the optimal probability distribution of additive noise in the restricted NP framework. Then, sufficient conditions for improvability and nonimprovability are derived in order to specify if additive noise can or cannot improve detection performance over scenarios in which no additive noise is employed. Also, for the special case of a finite number of possible parameter values under each hypothesis, it is shown that the optimal additive noise can be represented by a discrete random variable with a certain number of point masses. In addition, particular improvability conditions are derived for that special case. Finally, theoretical results are provided for a numerical example and improvements via additive noise are illustrated. © 2013 Elsevier Inc
Noise enhanced detection in restricted Neyman-Pearson framework
Noise enhanced detection is studied for binary composite hypothesis-testing problems in the presence of prior information uncertainty. The restricted Neyman-Pearson (NP) framework is considered, and a formulation is obtained for the optimal additive noise that maximizes the average detection probability under constraints on worst-case detection and false-alarm probabilities. In addition, sufficient conditions are provided to specify when the use of additive noise can or cannot improve performance of a given detector according to the restricted NP criterion. A numerical example is presented to illustrate the improvements obtained via additive noise. © 2012 IEEE
Alternative approaches and noise benefits in hypothesis-testing problems in the presence of partial information
Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 2011.Thesis (Ph. D.) -- Bilkent University, 2011.Includes bibliographical references leaves 153-164.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.Bayram, SuatPh.D
Noise Enhanced M-ary Composite Hypothesis-Testing in the Presence of Partial Prior Information
Cataloged from PDF version of article.In this correspondence, noise enhanced detection is 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 in order to investigate the theoretical results. © 2010 IEEE
Noise Enhanced Hypothesis-Testing in the Restricted Bayesian Framework
Cataloged from PDF version of article.Performance of some suboptimal detectors can be enhanced by adding independent noise to their observations. In this paper, the effects of additive noise are investigated 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 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
Noise enhanced detection in restricted Neyman-Pearson framework
Ankara : The Department of Electrical and Electronics Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Master's) -- Bilkent University, 2013.Includes bibliographical references leaves 37-40.Hypothesis tests frequently arise in many different engineering problems. Among
the most frequently used tests are Bayesian, minimax, and Neyman-Pearson.
Even though these tests are capable of addressing many real-life problems, they
can be insufficient in certain scenarios. For this reason, developing new hypothesis
tests is an important objective. One such developed test is the restricted NeymanPearson
test, where one tries to maximize the average detection probability while
keeping the worst-case detection and false-alarm probabilities bounded.
Finding the best hypothesis testing approach for a problem-at-hand is an important
point. Another important one is to employ a detector with an acceptable
performance. In particular, if the employed detector is suboptimal, it is crucial
that it meets the performance requirements. Previous research has proven that
performance of some suboptimal detectors can be improved by adding noise to
their inputs, which is known as noise enhancement.
In this thesis we investigate noise enhancement according to the restricted
Neyman-Pearson framework. To that aim, we formulate an optimization problem
for optimal additive noise. Then, generic improvability and nonimprovability
conditions are derived, which specify if additive noise can result in performance
improvements. We then analyze the special case in which the parameter space is
discrete and finite, and show that the optimal noise probability density function is
discrete with a certain number of point masses. The improvability results are also
extended and more precise conditions are derived. Finally, a numerical example
is provided which illustrates the theoretical results and shows the benefits of
applying noise enhancement to a suboptimal detector.Gültekin, ŞanM.S
Time-frequency detection algorithm for gravitational wave bursts
An efficient algorithm is presented for the identification of short bursts of
gravitational radiation in the data from broad-band interferometric detectors.
The algorithm consists of three steps: pixels of the time-frequency
representation of the data that have power above a fixed threshold are first
identified. Clusters of such pixels that conform to a set of rules on their
size and their proximity to other clusters are formed, and a final threshold is
applied on the power integrated over all pixels in such clusters. Formal
arguments are given to support the conjecture that this algorithm is very
efficient for a wide class of signals. A precise model for the false alarm rate
of this algorithm is presented, and it is shown using a number of
representative numerical simulations to be accurate at the 1% level for most
values of the parameters, with maximal error around 10%.Comment: 26 pages, 15 figures, to appear in PR
Stochastic resonance in binary composite hypothesis-testing problems in the Neyman-Pearson framework
Performance of some suboptimal detectors can be enhanced by adding independent noise to their inputs via the stochastic resonance (SR) effect. In this paper, the effects of SR are studied for binary composite hypothesis-testing problems. A Neyman-Pearson 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 to obtaining the probability distribution of optimal additive noise are discussed. Finally, a detection example is presented to investigate the theoretical results. © 2012 Elsevier Inc. All rights reserved
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