Measure transformed quasi likelihood ratio test for Bayesian binary hypothesis testing

Nir Halay, Koby Todros, Alfred O. Hero

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

In this paper, a generalization of the Gaussian quasi likelihood ratio test (GQLRT) for Bayesian binary hypothesis testing is developed. The proposed generalization, called measure-transformed GQLRT (MT-GQLRT), selects a Gaussian probability model that best empirically fits a transformed conditional probability measure of the data. By judicious choice of the transform we show that, unlike the GQLRT, the proposed test is resilient to outliers and involves higher-order statistical moments leading to significant mitigation of the model mismatch effect on the decision performance. Under some mild regularity conditions we show that the test statistic of the proposed MT-GQLRT is asymptotically normal. A data driven procedure for optimal selection of the measure transformation parameters is developed that minimizes an empirical estimate of the asymptotic Bayes risk. The MT-GQLRT is applied to signal classification in a simulation example that establishes significantly improved probability of error performance relative to the standard GQLRT.

Original languageEnglish
Title of host publication2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016
PublisherIEEE Computer Society
ISBN (Electronic)9781467378024
DOIs
StatePublished - 24 Aug 2016
Event19th IEEE Statistical Signal Processing Workshop, SSP 2016 - Palma de Mallorca, Spain
Duration: 25 Jun 201629 Jun 2016

Publication series

NameIEEE Workshop on Statistical Signal Processing Proceedings
Volume2016-August

Conference

Conference19th IEEE Statistical Signal Processing Workshop, SSP 2016
Country/TerritorySpain
CityPalma de Mallorca
Period25/06/1629/06/16

Keywords

  • Bayesian hypothesis testing
  • Signal classification
  • higher-order statistics
  • probability measure transform
  • robust statistics

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Applied Mathematics
  • Signal Processing
  • Computer Science Applications

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