On Divergence Measures Leading to Jeffreys and Other Reference Priors

Generalization of Jeffreys’ Divergence Based Priors for Bayesian Hypothesis testing

In this paper we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms and desirable properties, like information (finite sample) consistency; often, they are similar to other existing proposals like the intrinsic priors; moreov...

Dating divergence of Polystigma and other Sordariomycetes

Studies on the evolutionary history of ascomycetes in terms of time scale will help to understand historical patterns that shape their biodiversity. Until now most of dating studies of ascomycetes have focused on major events in fungal evolution but not on divergence events within smaller groups of fungi e.g. within Sordariomycetes. We used molecular dating to estimate the time of separation of...

A Note on Bound for Jensen-Shannon Divergence by Jeffreys

We present a lower bound on the Jensen-Shannon divergence by the Jeffrers’ divergence when pi ≥ qi is satisfied. In the original Lin's paper [IEEE Trans. Info. Theory, 37, 145 (1991)], where the divergence was introduced, the upper bound in terms of the Jeffreys was the quarter of it. In view of a recent shaper one reported by Crooks, we present a discussion on upper bounds by transcendental fu...

On Independent Reference Priors

Bounds on Nonsymmetric Divergence Measure in terms of Other Symmetric and Nonsymmetric Divergence Measures

Vajda (1972) studied a generalized divergence measure of Csiszar's class, so called "Chi-m divergence measure." Variational distance and Chi-square divergence are the special cases of this generalized divergence measure at m = 1 and m = 2, respectively. In this work, nonparametric nonsymmetric measure of divergence, a particular part of Vajda generalized divergence at m = 4, is taken and charac...