TY - JOUR

T1 - Optimal information usage in binary sequential hypothesis testing

AU - Doerpinghaus, Meik

AU - Neri, Izaak

AU - Roldan, Edgar

AU - Juelicher, Frank

N1 - Funding Information:
∗Received by the editors December 7, 2020; revised July 18, 2022; published electronically May 4, 2023. This work was partly supported by the German Research Foundation (DFG) within the Cluster of Excellence EXC 1056 “Center for Advancing Electronics Dresden (cfaed)” and within the CRC 912 “Highly Adaptive Energy-Efficient Computing (HAEC).” Originally published in the Russian journal Teoriya Veroyatnostei i ee Primeneniya, 68 (2023), pp. 93–105. https://doi.org/10.1137/S0040585X97T991295 †Vodafone Chair Mobile Communications Systems and Center for Advancing Electronics Dresden (cfaed), Technische Universität Dresden, Dresden, Germany (meik.doerpinghaus@tu-dresden.de). ‡Department of Mathematics, King’s College London, London, UK (izaak.neri@kcl.ac.uk). §ICTP — Abdus Salam International Centre for Theoretical Physics, Trieste, Italy (edgar@ictp. it). ¶Max-Planck-Institute for the Physics of Complex Systems, Dresden, Germany, and Center for Advancing Electronics Dresden (cfaed), Technische Universität Dresden, Dresden, Germany (julicher@pks.mpg.de).
Publisher Copyright:
© by SIAM. Unauthorized reproduction of this article is prohibited.

PY - 2023/5/4

Y1 - 2023/5/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85166197297&partnerID=8YFLogxK

U2 - 10.1137/S0040585X97T991295

DO - 10.1137/S0040585X97T991295

M3 - Article

SN - 1095-7219

VL - 68

SP - 77

EP - 87

JO - Theory of Probability and Its Applications

JF - Theory of Probability and Its Applications

IS - 1

ER -