On the Optimality of Likelihood Ratio Test for Prospect Theory-Based Binary Hypothesis Testing

Sinan Gezici, Pramod K. Varshney

Research output: Contribution to journalArticle

4 Scopus citations

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.

Original languageEnglish (US)
Article number8501545
Pages (from-to)1845-1849
Number of pages5
JournalIEEE Signal Processing Letters
Volume25
Issue number12
DOIs
StatePublished - Dec 2018

Keywords

  • Detection
  • hypothesis testing
  • likelihood ratio test
  • prospect theory
  • randomization

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics

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