Journal
THEORY OF PROBABILITY AND ITS APPLICATIONS
Volume 68, Issue 1, Pages 77-87Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0040585X97T991295
Keywords
sequential hypothesis testing; sequential probability ratio test; mutual information
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This passage discusses whether an information theoretic interpretation can be given to optimal algorithms in sequential hypothesis testing. The authors prove that for a 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 suggests that the sequential probability ratio test optimally utilizes the available hypothesis information in the observations. 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.
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 sequen-tial 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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