A Parametric Bayesian Approach in Density Ratio Estimation

Abdolnasser Sadeghkhani; Yingwei Peng; Devon Lin

doi:10.20944/preprints201903.0025.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 3 March 2019 / Approved: 4 March 2019 / Online: 4 March 2019 (09:43:12 CET)

This paper considers estimating the ratio of two distributions with different parameters and common supports. We consider a Bayesian approach based on the Log--Huber loss function which is resistant to outliers and useful to find robust M-estimators. We propose two different types of Bayesian density ratio estimators and compare their performance in terms of Bayesian risk function with themselves as well as the usual plug-in density ratio estimators. Some applications such as classification and divergence function estimation are addressed.

Bayes estimator, Bregman divergence, Density ratio, Exponential family, Log--Huber loss.

MATHEMATICS & COMPUTER SCIENCE, Probability and Statistics

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A Parametric Bayesian Approach in Density Ratio Estimation

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