{"title":"二值序列假设检验中的最优信息利用","authors":"M. Dörpinghaus, I. Neri, É. Roldán, F. Jülicher","doi":"10.1137/s0040585x97t991295","DOIUrl":null,"url":null,"abstract":"An interesting question is whether an information theoretic interpretation can be given of optimal algorithms in sequential hypothesis testing. We prove that for the binary sequential probability ratio test of a continuous observation process, the mutual information between the observation process up to the decision time and the actual hypothesis conditioned on the decision variable is equal to zero. This result can be interpreted as an optimal usage of the information on the hypothesis available in the observations by the sequential probability ratio test. As a consequence, the mutual information between the random decision time of the sequential probability ratio test and the actual hypothesis conditioned on the decision variable is also equal to zero.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimal Information Usage in Binary Sequential Hypothesis Testing\",\"authors\":\"M. Dörpinghaus, I. Neri, É. Roldán, F. Jülicher\",\"doi\":\"10.1137/s0040585x97t991295\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An interesting question is whether an information theoretic interpretation can be given of optimal algorithms in sequential hypothesis testing. We prove that for the binary sequential probability ratio test of a continuous observation process, the mutual information between the observation process up to the decision time and the actual hypothesis conditioned on the decision variable is equal to zero. This result can be interpreted as an optimal usage of the information on the hypothesis available in the observations by the sequential probability ratio test. As a consequence, the mutual information between the random decision time of the sequential probability ratio test and the actual hypothesis conditioned on the decision variable is also equal to zero.\",\"PeriodicalId\":51193,\"journal\":{\"name\":\"Theory of Probability and its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory of Probability and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/s0040585x97t991295\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/s0040585x97t991295","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Optimal Information Usage in Binary Sequential Hypothesis Testing
An interesting question is whether an information theoretic interpretation can be given of optimal algorithms in sequential hypothesis testing. We prove that for the binary sequential probability ratio test of a continuous observation process, the mutual information between the observation process up to the decision time and the actual hypothesis conditioned on the decision variable is equal to zero. This result can be interpreted as an optimal usage of the information on the hypothesis available in the observations by the sequential probability ratio test. As a consequence, the mutual information between the random decision time of the sequential probability ratio test and the actual hypothesis conditioned on the decision variable is also equal to zero.
期刊介绍:
Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.