二值序列假设检验中的最优信息利用

IF 0.5 4区 数学 Q4 STATISTICS & PROBABILITY
M. Dörpinghaus, I. Neri, É. Roldán, F. Jülicher
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引用次数: 0

摘要

一个有趣的问题是信息理论能否解释序列假设检验中的最优算法。证明了对于连续观测过程的二元序列概率比检验,观测过程到决策时间与以决策变量为条件的实际假设之间的互信息为零。这个结果可以解释为通过序列概率比检验对观测中可用的假设信息的最佳使用。因此,序列概率比检验的随机决策时间与以决策变量为条件的实际假设之间的互信息也为零。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.
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来源期刊
Theory of Probability and its Applications
Theory of Probability and its Applications 数学-统计学与概率论
CiteScore
1.00
自引率
16.70%
发文量
54
审稿时长
6 months
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.
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