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On the Limiting Behaviour of the Fundamental Geodesics of Information Geometry

Critchley, Frank and Marriott, Paul (2017). On the Limiting Behaviour of the Fundamental Geodesics of Information Geometry. Entropy, 19(10), article no. 524.

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DOI (Digital Object Identifier) Link: https://doi.org/10.3390/e19100524
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Abstract

The Information Geometry of extended exponential families has received much recent attention in a variety of important applications, notably categorical data analysis, graphical modelling and, more specifically, log-linear modelling. The essential geometry here comes from the closure of an exponential family in a high-dimensional simplex. In parallel, there has been a great deal of interest in the purely Fisher Riemannian structure of (extended) exponential families, most especially in the Markov chain Monte Carlo literature. These parallel developments raise challenges, addressed here, at a variety of levels: both theoretical and practical—relatedly, conceptual and methodological. Centrally to this endeavour, this paper makes explicit the underlying geometry of these two areas via an analysis of the limiting behaviour of the fundamental geodesics of Information Geometry, these being Amari’s (+1) and (0)-geodesics, respectively. Overall, a substantially more complete account of the Information Geometry of extended exponential families is provided than has hitherto been the case. We illustrate the importance and benefits of this novel formulation through applications.

Item Type: Journal Item
Copyright Holders: 2017 The Authors
ISSN: 1099-4300
Keywords: extended exponential families; information geometry; Riemannian Markov Chain Monte Carlo
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 52637
Depositing User: Frank Critchley
Date Deposited: 18 Dec 2017 10:23
Last Modified: 18 Dec 2017 10:31
URI: http://oro.open.ac.uk/id/eprint/52637
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