UNSPECIFIED. (2003) Stochastic factorizations, sandwiched simplices and the topology of the space of explanations. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 459 (2039). pp. 2821-2845. ISSN 1364-5021

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Abstract

We study the space of stochastic factorizations of a stochastic matrix V, motivated by the statistical problem of hidden random variables. We show that this space is homeomorphic to the space of simplices sandwiched between two nested convex polyhedra, and use this geometrical model to gain some insight into its structure and topology. We prove theorems describing its homotopy type, and, in the case where the rank of V is 2, we give a complete description, including bounds on the number of connected components, and examples in which these bounds are attained. We attempt to make the notions of topology accessible and relevant to statisticians.

Item Type:	Journal Article
Subjects:	Q Science
Journal or Publication Title:	PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Publisher:	ROYAL SOC LONDON
ISSN:	1364-5021
Date:	8 November 2003
Volume:	459
Number:	2039
Number of Pages:	25
Page Range:	pp. 2821-2845
Identification Number:	10.1098/rspa.2003.1150
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/9172

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