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Optimal information usage in binary sequential hypothesis testing

Research output: Contribution to journalArticlepeer-review

Meik Doerpinghaus, Izaak Neri, Edgar Roldan, Frank Juelicher

Original languageEnglish
Number of pages11
JournalTheory of Probability and Its Applications
Issue number1
Accepted/In press25 Aug 2022
Published4 May 2023


  • SeqHypoTesting

    SeqHypoTesting.pdf, 283 KB, application/pdf

    Uploaded date:22 Nov 2022

    Version:Accepted author manuscript

    Licence:CC BY

King's Authors


An interesting question is whether an information theoretical interpretation can be given to 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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