A Property of the Kullback--Leibler Divergence for Location-scale Models

2016/04/07 by Cristiano Villa, Villa, Cristiano · 1 citation
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.1604.01983

arxiv created 2016/04/07 · openalex publication_date 2016/04/07 · arxiv updated 2016/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we discuss a property of the Kullback--Leibler divergence measured between two models of the family of the location-scale distributions. We show that, if model M₁ and model M₂ are represented by location-scale distributions, then the minimum Kullback--Leibler divergence from M₁ to M₂, with respect to the parameters of M₂, is independent from the value of the parameters of M₁. Furthermore, we show that the property holds for models that can be transformed into location-scale distributions. We illustrate a possible application of the property in objective Bayesian model selection.

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