Algebraic/Infinite dimensional/Banach Information Manifolds

28/08/2013
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Algebraic/Infinite dimensional/Banach Information Manifolds

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Nonparametric Information Geometry Session: Algebraic/Infinite dimensional/Banach Information Manifolds Chair: Giovanni Pistone August 28, 2013 Talks • Asymptotically Efficient Estimators for Algebraic Statistical Manifolds. Kei Kobayashi and Henry P. Wynn • Infinite-Dimensional Manifolds of Finite-Entropy Probability Measures. Nigel J. Newton • Invariant geometric structures on statistical models. Hˆong Vˆan Lˆe • The ∆2-Condition and φ-Families of Probability Distributions. Rui F. Vigelis and Charles C. Cavalcante • A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences. G. Loaiza and H.R. Quiceno • Nihat Ay, J¨urgen Jost, Hˆong Vˆan Lˆe, and Lorenz Schwachh¨ofer. Information geometry and sufficient statistics. arXiv:1207.6736, 2013 Definition A k-integrable parametrized measure model is a quadruple (M, Ω, µ, p), where M is a smooth Banach manifold and p a map from the manifold M to the set M+(ω, µ) of all finite measures on Ω which are equivalent to µ, provided with the L1-topology, such that 1. the real function on M x → ¯p(x, ω) is Gateaux-differentiable for almost all ω, ¯p = dp/dµ. 2. for all 1 ≤ h ≤ k and all continuous vector field V on M the random variable ω → ∂V ¯p(x, ω) belongs to Lh(Ω, p(x)) and the function x → ∂V ¯p(x, ω) Lh(Ω,p(x)) is continuous on M.