A geometry on the space of probabilities. II: Projective spaces and exponential families

DOI10.4171/RMI/475zbMath1122.46039MaRDI QIDQ877797

Lázaro Recht, Henryk Gzyl

Publication date: 3 May 2007

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmi/1169480032

Mathematics Subject Classification ID

Foundations and philosophical topics in statistics (62A01) Probability distributions: general theory (60E05) Differential geometry of homogeneous manifolds (53C30) General theory of (C^*)-algebras (46L05) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Other complex differential geometry (53C56) Spaces of measures, convergence of measures (28A33) Measures of information, entropy (94A17) Connections (general theory) (53C05) Probability theory on algebraic and topological structures (60B99) Complex spaces with a group of automorphisms (32M99)

Related Items (2)

Parametric models and information geometry on \(W^\star\)-algebras ⋮ Geometry of the probability simplex and its connection to the maximum entropy method

Cites Work

• A geometry on the space of probabilities. I: The finite dimensional case
• Topics in statistical information theory
• The geometry of exponential families
• Theory of statistical inference and information. Transl. from the Slovak by the author
• The exponential statistical manifold: mean parameters, orthogonality and space transformations
• Exponential sets and their geometric motions
• Differential geometry of curved exponential families. Curvatures and information loss
• Conditional expectations and operator decompositions
• A infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one
• The geometry of the space of selfadjoint invertible elements in a \(C^*\)-algebra
• Information Theory and Statistical Mechanics
• CONNECTIONS ON STATISTICAL MANIFOLDS OF DENSITY OPERATORS BY GEOMETRY OF NONCOMMUTATIVE L^p-SPACES
• ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY
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