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Infinite-dimensional statistical manifolds based on a balanced chart

Newton, Nigel J (2016) 'Infinite-dimensional statistical manifolds based on a balanced chart.' Bernoulli, 22 (2). 711 - 731. ISSN 1350-7265

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We develop a family of infinite-dimensional Banach manifolds of measures on an abstract measurable space, employing charts that are balanced between the density and log-density functions. The manifolds, (Mλ,λ e [2,∞)), retain many of the features of finite-dimensional information geometry; in particular, the α-divergences are of class C[λ]-1, enabling the definition of the Fisher metric and α-derivatives of particular classes of vector fields. Manifolds of probability measures, (Mλ,λ e [2,∞)), based on centred versions of the charts are shown to be C[λ]-1-embedded submanifolds of the. Mλ. The Fisher metric is a pseudo-Riemannian metric on. Mλ. However, when restricted to finite-dimensional embedded submanifolds it becomes a Riemannian metric, allowing the full development of the geometry of α-covariant derivatives. Mλ and Mλ provide natural settings for the study and comparison of approximations to posterior distributions in problems of Bayesian estimation.

Item Type: Article
Uncontrolled Keywords: Banach manifold; Bayesian estimation; Fisher metric; information geometry; non-parametric statistics
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Jim Jamieson
Date Deposited: 23 Jul 2015 14:35
Last Modified: 15 Jan 2020 17:15

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