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

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Abstract

© 2016 ISI/BS. 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
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:	29 Nov 2017 05:15
URI:	http://repository.essex.ac.uk/id/eprint/14436

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