A Characterization of the Likelihood Ratio Order in Terms of Mixtures

• Activity Number: 355 - Advanced Bayesian Topics (Part 4)
• Type: Contributed
• Date/Time: Thursday, August 12, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Michael Jauch*
• Companies: Cornell University
• Keywords: likelihood ratio order; density estimation; hypothesis testing; stochastic order; nonparametric; Bayesian

Abstract

The likelihood ratio plays an important role in statistical theory and also in practice. In applied contexts, it is often assumed that a pair of probability distributions satisfies a likelihood ratio order. Statistical inference is challenging in this setting due to the likelihood ratio constraint. To address this problem, we present a novel characterization of the likelihood ratio order in terms of mixtures which allows for unconstrained inference. We illustrate its utility in Bayesian nonparametric density estimation and hypothesis testing.