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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Abstract
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 |
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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 |
URI: | http://repository.essex.ac.uk/id/eprint/14436 |
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