Differential Geometrical Theory of Statistics by Frédéric BarbarescoDifferential Geometrical Theory of Statistics by Frédéric Barbaresco

Differential Geometrical Theory of Statistics

Guest editorFrédéric Barbaresco, Frank NIELSEN

Paperback | June 6, 2017

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This Special Issue "Differential Geometrical Theory of Statistics" collates selected invited and contributed talks presented during the conference GSI'15 on "Geometric Science of Information" which was held at the Ecole Polytechnique, Paris-Saclay Campus, France, in October 2015 (Conference web site: http://www.see.asso.fr/gsi2015).

Title:Differential Geometrical Theory of StatisticsFormat:PaperbackProduct dimensions:472 pages, 9.61 × 6.69 × 1.28 inShipping dimensions:9.61 × 6.69 × 1.28 inPublished:June 6, 2017Publisher:MDPI AGLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3038424242

ISBN - 13:9783038424246


Table of Contents

1) From Tools in Symplectic and Poisson Geometry to J.-M. Souriau’s Theories of Statistical Mechanics and Thermodynamics
2) Geometric Theory of Heat from Souriau Lie Groups Thermodynamics and Koszul Hessian Geometry: Applications in Information Geometry for Exponential Families
3) Link between Lie Group Statistical Mechanics and Thermodynamics of Continua
4) Foliations-Webs-Hessian Geometry-Information Geometry-Entropy and Cohomology
5) Explicit Formula of Koszul–Vinberg Characteristic Functions for a Wide Class of Regular Convex Cones
6) A Proximal Point Algorithm for Minimum Divergence Estimators with Application to
Mixture Models
7) Geometry Induced by a Generalization of Rényi Divergence
8) Guaranteed Bounds on Information-Theoretic Measures of Univariate Mixtures Using Piecewise
Log-Sum-Exp Inequalities
9) A Sequence of Escort Distributions and Generalizations of Expectations on q-Exponential Family
10) The Information Geometry of Sparse Goodness-of-Fit Testing
11) Kernel Density Estimation on the Siegel Space with an Application to Radar Processing
12) Riemannian Laplace Distribution on the Space of Symmetric Positive Definite Matrices
13) Entropy Minimizing Curves with Application to Flight Path Design and Clustering
14) Anisotropically Weighted and Nonholonomically Constrained Evolutions on Manifolds
15) Non-Asymptotic Confidence Sets for Circular Means
16) Syntactic Parameters and a Coding Theory Perspective on Entropy and Complexity of Language Families