Related papers: Geometry of escort distributions
We introduce a new transformation called \emph{relative differential-escort}, which extends the usual differential-escort transformation by relating the change of variable to a reference probability density. As an application of it, we…
We evaluate generalized information measures constructed with Husimi distributions and connect them with the Wehrl entropy, on the one hand, and with thermal uncertainty relations, on the other one. The concept of escort distribution plays…
We study the geometry of probability distributions with respect to a generalized family of Csisz\'ar $f$-divergences. A member of this family is the relative $\alpha$-entropy which is also a R\'enyi analog of relative entropy in information…
We give a simple probabilistic description of a transition between two states which leads to a generalized escort distribution. When the parameter of the distribution varies, it defines a parametric curve that we call an escort-path. The…
This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many…
We propose the generalised Fisher information or the one-parameter extended class of the Fisher information for the case of one random variable. This new form of the Fisher information is obtained from the intriguing connection between the…
We present an argument about the origin of escort distributions used in conjunction with the q-entropy in non-additive thermo-statistics. The origin of the escort distributions is ascribed to the fact that the effective statistical…
When dealing with a parametric statistical model, a Riemannian manifold can naturally appear by endowing the parameter space with the Fisher information metric. The geometry induced on the parameters by this metric is then referred to as…
Choosing the Fisher information as the metric tensor for a Riemannian manifold provides a powerful yet fundamental way to understand statistical distribution families. Distances along this manifold become a compelling measure of statistical…
The lower bound of Cramer and Rao is generalized to pairs of families of probability distributions, one of which is escort to the other. This bound is optimal for certain families, called phi-exponential in the paper. Their dual structure…
The nonparametric view of Bayesian inference has transformed statistics and many of its applications. The canonical Dirichlet process and other more general families of nonparametric priors have served as a gateway to solve frontier…
The Fisher-Rao metric from Information Geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of Information Geometry to study more general phase transitions in…
Bayesian predictive densities when the observed data $x$ and the target variable $y$ to be predicted have different distributions are investigated by using the framework of information geometry. The performance of predictive densities is…
Superpositions of different statistics on different time or spatial scales (in short, superstatistics) can naturally lead to an effective description by nonextensive statistical mechanics. We first discuss the role of escort distributions…
We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…
In this paper, we investigate the Fisher-Rao geometry of the two-parameter family of Pareto distribution. We prove that its geometrical structure is isometric to the Poincar\'e upper half-plane model, and then study the corresponding…
We propose a novel Riemannian geometric framework for variational inference in Bayesian models based on the nonparametric Fisher-Rao metric on the manifold of probability density functions. Under the square-root density representation, the…
Singular statistical models arise whenever different parameter values induce the same distribution, leading to non-identifiability and a breakdown of classical asymptotic theory. While existing approaches analyze these phenomena in…
A family of replicator-like dynamics, called the escort replicator equation, is constructed using information-geometric concepts and generalized information entropies and diverenges from statistical thermodynamics. Lyapunov functions and…
Parametrized families of density operators are studied. A generalization of the lower bound of Cramer and Rao is formulated. It involves escort density operators. The notion of phi-exponential family is introduced. This family, together…