Neighbourhoods of independence and associated geometry

Arwini, Khadiga and Dodson, CTJ (2005) Neighbourhoods of independence and associated geometry. [MIMS Preprint]

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Abstract

We provide explicit information geometric tubular neighbourhoods containing all bivariate processes sufficiently close to the cases of independent Poisson or Gaussian processes. This is achieved via affine immersions of the 4-manifold of Freund bivariate distributions and of the 5-manifold of bivariate Gaussians. We provide also the alpha-geometry for both manifolds. The Central Limit Theorem makes our neighbourhoods of independence limiting cases for a wide range of bivariate processes; the topological character of the results makes them stable under small perturbations, which is important for applications.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	information geometry, statistical manifold, neighbourhoods of independence, exponential distribution, Freund distribution, Gaussian distribution
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User:	Prof CTJ Dodson
Date Deposited:	13 Dec 2005
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/121

Available Versions of this Item

• Neighbourhoods of independence and associated geometry. (deposited 13 Dec 2005) [Currently Displayed]
  • Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussians and Freund distributions. (deposited 04 Jun 2007)

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