Noise Enhancement for Weighted Sum of Type I and II Error Probabilities with Constraints
In this paper, the noise-enhanced detection problem is investigated for the binary hypothesis-testing. The optimal additive noise is determined according to a criterion proposed by DeGroot and Schervish (2011), which aims to minimize the weighted sum of type I and II error probabilities under constr...
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| Format: | Article |
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MDPI AG
2017-06-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/19/6/276 |
| _version_ | 1811305087410110464 |
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| author | Shujun Liu Ting Yang Kui Zhang |
| author_facet | Shujun Liu Ting Yang Kui Zhang |
| author_sort | Shujun Liu |
| collection | DOAJ |
| description | In this paper, the noise-enhanced detection problem is investigated for the binary hypothesis-testing. The optimal additive noise is determined according to a criterion proposed by DeGroot and Schervish (2011), which aims to minimize the weighted sum of type I and II error probabilities under constraints on type I and II error probabilities. Based on a generic composite hypothesis-testing formulation, the optimal additive noise is obtained. The sufficient conditions are also deduced to verify whether the usage of the additive noise can or cannot improve the detectability of a given detector. In addition, some additional results are obtained according to the specificity of the binary hypothesis-testing, and an algorithm is developed for finding the corresponding optimal noise. Finally, numerical examples are given to verify the theoretical results and proofs of the main theorems are presented in the Appendix. |
| first_indexed | 2024-04-13T08:18:56Z |
| format | Article |
| id | doaj.art-69719fc81c6f43019b8ce168d0d91b4c |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T08:18:56Z |
| publishDate | 2017-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-69719fc81c6f43019b8ce168d0d91b4c2022-12-22T02:54:42ZengMDPI AGEntropy1099-43002017-06-0119627610.3390/e19060276e19060276Noise Enhancement for Weighted Sum of Type I and II Error Probabilities with ConstraintsShujun Liu0Ting Yang1Kui Zhang2College of Communication Engineering, Chongqing University, Chongqing 400044, ChinaCollege of Communication Engineering, Chongqing University, Chongqing 400044, ChinaCollege of Communication Engineering, Chongqing University, Chongqing 400044, ChinaIn this paper, the noise-enhanced detection problem is investigated for the binary hypothesis-testing. The optimal additive noise is determined according to a criterion proposed by DeGroot and Schervish (2011), which aims to minimize the weighted sum of type I and II error probabilities under constraints on type I and II error probabilities. Based on a generic composite hypothesis-testing formulation, the optimal additive noise is obtained. The sufficient conditions are also deduced to verify whether the usage of the additive noise can or cannot improve the detectability of a given detector. In addition, some additional results are obtained according to the specificity of the binary hypothesis-testing, and an algorithm is developed for finding the corresponding optimal noise. Finally, numerical examples are given to verify the theoretical results and proofs of the main theorems are presented in the Appendix.http://www.mdpi.com/1099-4300/19/6/276noise enhancementhypothesis testingweighted sumerror probability |
| spellingShingle | Shujun Liu Ting Yang Kui Zhang Noise Enhancement for Weighted Sum of Type I and II Error Probabilities with Constraints Entropy noise enhancement hypothesis testing weighted sum error probability |
| title | Noise Enhancement for Weighted Sum of Type I and II Error Probabilities with Constraints |
| title_full | Noise Enhancement for Weighted Sum of Type I and II Error Probabilities with Constraints |
| title_fullStr | Noise Enhancement for Weighted Sum of Type I and II Error Probabilities with Constraints |
| title_full_unstemmed | Noise Enhancement for Weighted Sum of Type I and II Error Probabilities with Constraints |
| title_short | Noise Enhancement for Weighted Sum of Type I and II Error Probabilities with Constraints |
| title_sort | noise enhancement for weighted sum of type i and ii error probabilities with constraints |
| topic | noise enhancement hypothesis testing weighted sum error probability |
| url | http://www.mdpi.com/1099-4300/19/6/276 |
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