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Computer Science > Information Theory

arXiv:1810.08469 (cs)
[Submitted on 19 Oct 2018]

Title:On the optimality of likelihood ratio test for prospect theory based binary hypothesis testing

Authors:Sinan Gezici, Pramod K. Varshney
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Abstract:In this letter, the optimality of the likelihood ratio test (LRT) is investigated for binary hypothesis testing problems in the presence of a behavioral decision-maker. By utilizing prospect theory, a behavioral decision-maker is modeled to cognitively distort probabilities and costs based on some weight and value functions, respectively. It is proved that the LRT may or may not be an optimal decision rule for prospect theory based binary hypothesis testing and conditions are derived to specify different scenarios. In addition, it is shown that when the LRT is an optimal decision rule, it corresponds to a randomized decision rule in some cases; i.e., nonrandomized LRTs may not be optimal. This is unlike Bayesian binary hypothesis testing in which the optimal decision rule can always be expressed in the form of a nonrandomized LRT. Finally, it is proved that the optimal decision rule for prospect theory based binary hypothesis testing can always be represented by a decision rule that randomizes at most two LRTs. Two examples are presented to corroborate the theoretical results.
Comments: 5 pages, 2 figures, to appear in IEEE SPL
Subjects: Information Theory (cs.IT)
Cite as: arXiv:1810.08469 [cs.IT]
  (or arXiv:1810.08469v1 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.1810.08469
Related DOI: https://doi.org/10.1109/LSP.2018.2877048

Submission history

From: Sinan Gezici [view email]
[v1] Fri, 19 Oct 2018 12:41:57 UTC (78 KB)
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