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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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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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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FREE EXPONENTIAL FAMILIES AS KERNEL FAMILIES [PDF]
Demonstratio Mathematica, 2009 AbstractFree exponential families have been previously introduced as a special case of ...
Włodzimierz Bryc
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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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Uniform Exponential Stability of Discrete Evolution Families on Space of p-Periodic Sequences [PDF]
Abstract and Applied Analysis, 2014 We prove that the discrete system ζn+1=Anζn is uniformly exponentially stable if and only if the unique solution of the Cauchy problem ζn+1=Anζn+eiθn+1zn+1, n∈Z+, ζ0=0, is bounded for any real number θ and any p-periodic sequence z(n) with z(0)=0. Here,
Yongfang Wang +4 more
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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 $X : E\{E(X|\theta)|X = x\} = ax + b$.
Persi Diaconis
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Stratified exponential families: Graphical models and model selection [PDF]
Annals of Statistics, 2001 Dan Geiger +3 more
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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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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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