Geometric Modeling in Probability and Statistics

DOI10.1007/978-3-319-07779-6zbMath1325.60001OpenAlexW595145996MaRDI QIDQ5168405

Constantin Udrişte, Ovidiu Calin

Publication date: 4 July 2014

Full work available at URL: https://doi.org/10.1007/978-3-319-07779-6

zbMATH Keywords

Riemannian metricdifferentiable manifoldsstatistical modeldifferential geometryinformation geometrygeometric modelingstatistical manifoldsFisher information metric

Mathematics Subject Classification ID

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory (60-01) Geodesics in global differential geometry (53C22) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry (53-01) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Statistical aspects of information-theoretic topics (62B10) Local Riemannian geometry (53B20) General theory of mathematical modeling (00A71) Geometric probability and stochastic geometry (60D99)

Related Items (33)

A new approach to gradient Ricci solitons and generalizations ⋮ Geometry and control of thermodynamic systems described by generalized exponential families ⋮ Semi-symmetric non-metric connections on statistical manifolds ⋮ Lifting statistical structures ⋮ On lightlike geometry of indefinite Sasakian statistical manifolds ⋮ A study of Rényi entropy based on the information geometry formalism ⋮ On a constant curvature statistical manifold ⋮ Pseudo-Riemannian geometry encodes information geometry in optimal transport ⋮ OPTIMAL CONTROL ON RELIABILITY PROBLEMS ⋮ Stochastic accessibility on Grushin-type manifolds ⋮ Generalized conjugate connections and equiaffine structures on semi-Riemannian manifolds ⋮ Anti-invariant holomorphic statistical submersions ⋮ Musical isomorphisms and statistical manifolds ⋮ Half a century of information geometry, part 1 ⋮ The Kullback-Leibler divergence between lattice Gaussian distributions ⋮ The Fisher-Rao loss for learning under label noise ⋮ Geometric properties of beta distributions ⋮ Complete integrability of gradient systems on a manifold admitting a potential in odd dimension ⋮ On a torsion/curvature analogue of dual connections and statistical manifolds ⋮ On the geometry of lightlike submanifolds of indefinite statistical manifolds ⋮ Unnamed Item ⋮ Logarithmic divergences from optimal transport and Rényi geometry ⋮ Geometry of the probability simplex and its connection to the maximum entropy method ⋮ Curvatures of semi-symmetric metric connections on statistical manifolds ⋮ Assignment Flows ⋮ Unnamed Item ⋮ Asymptotic expansion of the risk of maximum likelihood estimator with respect to α-divergence ⋮ Exponentially concave functions and a new information geometry ⋮ Fisher-Rao geometry of Dirichlet distributions ⋮ On the geometric structure ofsome statistical manifolds ⋮ Monte Carlo Information-Geometric Structures ⋮ Clustering in Hilbert’s Projective Geometry: The Case Studies of the Probability Simplex and the Elliptope of Correlation Matrices ⋮ Optimal information, Jensen-RIG function and \(\alpha\)-Onicescu's correlation coefficient in terms of information generating functions

This page was built for publication: Geometric Modeling in Probability and Statistics