Exponential Families with External Parameters [PDF]
Entropy, 2022 In this paper we introduce a class of statistical models consisting of exponential families depending on additional parameters, called external parameters.
Marco Favretti
doaj +7 more sources
Revisiting Chernoff Information with Likelihood Ratio Exponential Families [PDF]
Entropy, 2022 The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance.
Frank Nielsen
doaj +4 more sources
Statistical Divergences between Densities of Truncated Exponential Families with Nested Supports: Duo Bregman and Duo Jensen Divergences [PDF]
Entropy, 2022 By calculating the Kullback–Leibler divergence between two probability measures belonging to different exponential families dominated by the same measure, we obtain a formula that generalizes the ordinary Fenchel–Young divergence.
Frank Nielsen
doaj +4 more sources
Deformed Algebras and Generalizations of Independence on Deformed Exponential Families [PDF]
Entropy, 2015 A deformed exponential family is a generalization of exponential families. Since the useful classes of power law tailed distributions are described by the deformed exponential families, they are important objects in the theory of complex systems.
Hiroshi Matsuzoe, Tatsuaki Wada
doaj +3 more sources
Conjugate Priors for Exponential Families
Annals of Statistics, 1979 Let $X$ be a random vector distributed according to an exponential family with natural parameter $\theta \in \Theta$. We characterize conjugate prior measures on $\Theta$ through the property of linear posterior expectation of the mean parameter of $X : E\{E(X|\theta)|X = x\} = ax + b$.
Donald Ylvisaker
exaly +5 more sources
On Representations of Divergence Measures and Related Quantities in Exponential Families [PDF]
Entropy, 2021 Within exponential families, which may consist of multi-parameter and multivariate distributions, a variety of divergence measures, such as the Kullback–Leibler divergence, the Cressie–Read divergence, the Rényi divergence, and the Hellinger metric, can ...
Stefan Bedbur, Udo Kamps
doaj +2 more sources
Networked Exponential Families for Big Data Over Networks
IEEE Access, 2020 The data generated in many application domains can be modeled as big data over networks, i.e., massive collections of high-dimensional local datasets related via an intrinsic network structure.
Alexander Jung
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Information Geometric Duality of ϕ-Deformed Exponential Families [PDF]
Entropy, 2019 In the world of generalized entropies—which, for example, play a role in physical systems with sub- and super-exponential phase space growth per degree of freedom—there are two ways for implementing constraints in the maximum entropy ...
Jan Korbel, Rudolf Hanel, Stefan Thurner
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Chentsov’s theorem for exponential families [PDF]
Information Geometry, 2017 Chentsov’s theorem characterizes the Fisher information metric on statistical models as the only Riemannian metric (up to rescaling) that is invariant under sufficient statistics.
J. Dowty
semanticscholar +5 more sources
Information Geometry of κ-Exponential Families: Dually-Flat, Hessian and Legendre Structures [PDF]
Entropy, 2018 In this paper, we present a review of recent developments on the κ -deformed statistical mechanics in the framework of the information geometry.
Antonio M. Scarfone +2 more
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