Informative Geometry of Probability Spaces
Informative Geometry of Probability Spaces
The paper deals with the geometrical properties that are induced by the local information content and structures of the parameter space of probability distributions. In this investigation the Rao distance which is the geodesic distance induced by the differential metric associated with the Fisher matrix of the parameter space, plays a major role. Moreover, some affine connections in this informative geometry of the parameter space are studied and thereby elucidating the role of curvature in statistical studies. In addition, closed form expressions for the Rao distances of certain families of probability distributions are given and discussed.
informative geometry, closed form expressions, Rao distance, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, information metric, Statistical aspects of information-theoretic topics, Information theory (general), Fisher matrix, measure of dissimilarity, univariate and multivariate distributions, Hilbert space embedding, curvature, Probability distributions: general theory, Geometric probability and stochastic geometry, local information content, multivariate normal, parameter space, geodesic distance
informative geometry, closed form expressions, Rao distance, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, information metric, Statistical aspects of information-theoretic topics, Information theory (general), Fisher matrix, measure of dissimilarity, univariate and multivariate distributions, Hilbert space embedding, curvature, Probability distributions: general theory, Geometric probability and stochastic geometry, local information content, multivariate normal, parameter space, geodesic distance
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