A geometry on the space of probabilities (II). Projective spaces and exponential families.

Gzyl, Henryk, and Recht, Lázaro. "A geometry on the space of probabilities (II). Projective spaces and exponential families.." Revista Matemática Iberoamericana 22.3 (2006): 833-849. <http://eudml.org/doc/41994>.

@article{Gzyl2006,
abstract = {In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points 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 shall develop everything in a generic C*-algebra setting, but shall have the function space model in mind.},
author = {Gzyl, Henryk, Recht, Lázaro},
journal = {Revista Matemática Iberoamericana},
keywords = {C*-álgebras; Espacios de probabilidad; Geodésicas; Espacio proyectivo; Familia exponencial; Geometría diferencial global},
language = {eng},
number = {3},
pages = {833-849},
title = {A geometry on the space of probabilities (II). Projective spaces and exponential families.},
url = {http://eudml.org/doc/41994},
volume = {22},
year = {2006},
}

TY - JOUR
AU - Gzyl, Henryk
AU - Recht, Lázaro
TI - A geometry on the space of probabilities (II). Projective spaces and exponential families.
JO - Revista Matemática Iberoamericana
PY - 2006
VL - 22
IS - 3
SP - 833
EP - 849
AB - In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points 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 shall develop everything in a generic C*-algebra setting, but shall have the function space model in mind.
LA - eng
KW - C*-álgebras; Espacios de probabilidad; Geodésicas; Espacio proyectivo; Familia exponencial; Geometría diferencial global
UR - http://eudml.org/doc/41994
ER -