Newton, Nigel J (2016) Infinite-dimensional statistical manifolds based on a balanced chart. Bernoulli, 22 (2). pp. 711-731. DOI https://doi.org/10.3150/14-BEJ673
Newton, Nigel J (2016) Infinite-dimensional statistical manifolds based on a balanced chart. Bernoulli, 22 (2). pp. 711-731. DOI https://doi.org/10.3150/14-BEJ673
Newton, Nigel J (2016) Infinite-dimensional statistical manifolds based on a balanced chart. Bernoulli, 22 (2). pp. 711-731. DOI https://doi.org/10.3150/14-BEJ673
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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Additional Information: | Published at http://dx.doi.org/10.3150/14-BEJ673 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm) |
Uncontrolled Keywords: | Banach manifold; Bayesian estimation; Fisher metric; information geometry; non-parametric statistics |
Subjects: | Q Science > QA Mathematics |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Computer Science and Electronic Engineering, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 23 Jul 2015 14:35 |
Last Modified: | 30 Oct 2024 20:04 |
URI: | http://repository.essex.ac.uk/id/eprint/14436 |
Available files
Filename: euclid.bj.1447077759.pdf