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
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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
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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
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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
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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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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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Information Geometry and Asymptotic Theory for SMML Estimators [PDF]
EntropyStrict minimum message length (SMML) is an information-theoretic coding principle that represents a continuous statistical model by a finite set of assertions and a partition of the sample space.
Enes Makalic, Daniel F. Schmidt
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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
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Two Families of Continuous Probability Distributions Generated by the Discrete Lindley Distribution
Mathematics, 2023 In this paper, we construct two new families of distributions generated by the discrete Lindley distribution. Some mathematical properties of the new families are derived. Some special distributions from these families can be constructed by choosing some
Srdjan Kadić +2 more
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Satisfiability with Exponential Families [PDF]
, 2007 Fix a set S ⊆ {0, 1}* of exponential size, e.g. |S ∩ {0, 1}n| ∈ Ω(αn), α > 1. The S-SAT problem asks whether a propositional formula F over variables v1, . . . , vn has a satisfying assignment (v1, . . . , vn) ∈ {0, 1}n ∩ S. Our interest is in determining the complexity of S-SAT.
Dominik Scheder, Philipp Zumstein
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