A geometry on the space of probabilities. I: The finite dimensional case
type: Item
instance of: scholarly article
title: A geometry on the space of probabilities. I: The finite dimensional case
zbMATH Open document ID: 1121.46043
DOI: 10.4171/RMI/465
published in: Revista Matemática Iberoamericana
publication date: 2007-05-14T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1161871347
full work available at URL: https://eudml.org/doc/41983
review text: Summary: We provide a natural way of defining exponential coordinates on the class of probabilities on the set \(\Omega = [1,n]\) or on \(\mathbb{P} = \{p=(p_1,\dots,p_n)\in \mathbb{R}^n \mid p_i > 0;\;\Sigma_{i=1}^n p_i =1\}\). For that, we have to regard \(\mathbb{P}\) as a projective space and the exponential coordinates will be related to geodesic flows in \(\mathbb{C}^n\). [Part II has appeared ibid.\ 22, No.\,3, 833--849 (2006; Zbl 1122.46039).]
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 28A33
Mathematics Subject Classification ID: 46L99
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 5152582
zbMATH Keywords: \(C^*\)-algebra
zbMATH Keywords: reductive homogeneous space
zbMATH Keywords: lifting of geodesics
zbMATH Keywords: exponential families
zbMATH Keywords: maximum entropy method
author: Henryk Gzyl
author: Lázaro Recht
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5152582