二值序列假设检验中的最优信息利用

Pub Date : 2023-05-01 DOI:10.1137/s0040585x97t991295
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。
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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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