On the Restricted Neyman–Pearson Approach for Composite Hypothesis-Testing in Presence of Prior Distribution Uncertainty

Bayram, Suat; Gezici, Sinan

doi:10.1109/tsp.2011.2153846

Cited by 17 publications

(37 citation statements)

References 43 publications

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“…In this paper, we propose an optimal spectrum sensing approach in the presence of prior distribution uncertainty (i.e., imperfect prior information) based on the restricted NeymanPearson (NP) approach [13]- [15]. Specifically, a composite hypothesis-testing problem in the NP framework is formulated, and uncertainties in prior distributions are taken into account via the restricted NP approach.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the aim in this study is to perform optimal spectrum sensing in the presence of uncertainties in the prior distribution of the unknown parameter related to the primary users. To achieve this aim, we adopt the restricted NP approach [13], [15] for this problem.…”

Section: Introductionmentioning

confidence: 99%

“…A restricted NP decision rule maximizes the average detection probability, which is obtained based on the imperfect PDF w(θ), under constraints on the worst-case detection and false-alarm probabilities. Mathematically stated, it is obtained as the solution of the following optimization problem [15]:…”

Section: Introductionmentioning

confidence: 99%

“…where λ ∈ [0, 1] is a design parameter that is set according to β [15]. Based on (1), the detection probability and the false-alarm probability in (6) are given by…”

Section: Introductionmentioning

confidence: 99%

“…The optimal solution to the problem in (3)- (5) is in the form of an NP decision rule corresponding to the least-favorable distribution [13]- [15]. The least-favorable distribution can be obtained by combining the uncertain PDF w(θ) with another…”

Section: Introductionmentioning

confidence: 99%

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Spectrum sensing via restricted Neyman-Pearson approach in the presence of non-Gaussian noise

Turgut

Gezici

2013

Eurocon 2013

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Abstract-In this paper, spectrum sensing in cognitive radio systems is studied for non-Gaussian channels in the presence of prior distribution uncertainty. In most practical cases, some amount of prior information about signals of primary users is available to secondary users but that information is never perfect. In order to design optimal spectrum sensing algorithms in such cases, we propose to employ the restricted Neyman-Pearson (NP) approach, which maximizes the average detection probability under constraints on the worst-case detection and false-alarm probabilities. We derive a restricted NP based spectrum sensing algorithm for additive Gaussian mixture noise channels, and compare its performance against the generalized likelihood ratio test (GLRT) and the energy detector. Simulation results show that the proposed spectrum sensing algorithm provides improvements over the other approaches in terms of minimum (worst-case) and/or average detection probabilities.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…where λ ∈ [0, 1] is a design parameter that is set according to β [15]. Based on (1), the detection probability and the false-alarm probability in (6) are given by…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spectrum sensing via restricted Neyman-Pearson approach in the presence of non-Gaussian noise

Turgut

Gezici

2013

Eurocon 2013

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Robust incorporation of historical information with known type I error rate inflation

Calderazzo,

Wiesenfarth,

Kopp‐Schneider

2023

Biometrical J

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Bayesian clinical trials can benefit from available historical information through the specification of informative prior distributions. Concerns are however often raised about the potential for prior‐data conflict and the impact of Bayes test decisions on frequentist operating characteristics, with particular attention being assigned to inflation of type I error (TIE) rates. This motivates the development of principled borrowing mechanisms, that strike a balance between frequentist and Bayesian decisions. Ideally, the trust assigned to historical information defines the degree of robustness to prior‐data conflict one is willing to sacrifice. However, such relationship is often not directly available when explicitly considering inflation of TIE rates. We build on available literature relating frequentist and Bayesian test decisions, and investigate a rationale for inflation of TIE rate which explicitly and linearly relates the amount of borrowing and the amount of TIE rate inflation in one‐arm studies. A novel dynamic borrowing mechanism tailored to hypothesis testing is additionally proposed. We show that, while dynamic borrowing prevents the possibility to obtain a simple closed‐form TIE rate computation, an explicit upper bound can still be enforced. Connections with the robust mixture prior approach, particularly in relation to the choice of the mixture weight and robust component, are made. Simulations are performed to show the properties of the approach for normal and binomial outcomes, and an exemplary application is demonstrated in a case study.

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Stochastic resonance in binary composite hypothesis-testing problems in the Neyman–Pearson framework

Bayram

Gezici

2012

Digital Signal Processing

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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.

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On the Restricted Neyman–Pearson Approach for Composite Hypothesis-Testing in Presence of Prior Distribution Uncertainty

Cited by 17 publications

References 43 publications

Spectrum sensing via restricted Neyman-Pearson approach in the presence of non-Gaussian noise

Spectrum sensing via restricted Neyman-Pearson approach in the presence of non-Gaussian noise

Robust incorporation of historical information with known type I error rate inflation

Stochastic resonance in binary composite hypothesis-testing problems in the Neyman–Pearson framework

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