A geometry on the space of probabilities. II: Projective spaces and exponential families
type: Item
instance of: scholarly article
title: A geometry on the space of probabilities. II: Projective spaces and exponential families
zbMATH Open document ID: 1122.46039
DOI: 10.4171/RMI/475
published in: Revista Matemática Iberoamericana
publication date: 2007-05-03T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1169480032
full work available at URL: https://eudml.org/doc/41994
review text: Summary: We continue a theme taken up in Part I, see [\textit{H.\,Gzyl} and \textit{L.\,Recht}, Rev.\ Mat.\ Iberom.\ 22, 545--558 (2006; Zbl 1121.46043)], namely, to provide a geometric interpretation of exponential families as endpoints of geodesics of a non-metric connection in a function space. For that, we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a homogeneous reductive space in the class of all bounded complex valued functions. We develop everything in a generic \({\mathcal C}^*\)-algebra setting, but have the function space model in mind.
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 53C56
Mathematics Subject Classification ID: 60B99
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 32M99
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 94A17
Mathematics Subject Classification ID: 58B20
Mathematics Subject Classification ID: 28A33
zbMATH DE Number: 5149120
author: Henryk Gzyl
author: Lázaro Recht
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5149120