Sinan Gezici (Bilkent University)

Math & Stats Department Colloquium
Friday, January 10, 2025

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Sinan Gezici (Bilkent University)

Title: Optimal Decision Rules for Hypothesis Testing Problems under General Criterion Involving Error Probabilities

Abstract: In this talk, we consider M-ary hypothesis-testing problems and characterize optimal decision rules under general criterion involving pairwise error probabilities, where likelihood ratios are employed as sufficient statistics. It is proved that an optimal decision rule can be obtained as a randomization between at most two deterministic decision rules in certain cases while a randomization among at most M(M-1)+1 deterministic decision rules can be required in other cases for optimality. We focus on some special cases of this generic approach such as prospect theory based hypothesis testing, where behavioral decision-makers distort probabilities and costs. We investigate the optimality of the likelihood ratio test (LRT) for prospect theory based binary hypothesis testing, and show that randomization of LRTs can be required for optimality. We provide various detection examples to illustrate the results.