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

Revista Matemática Iberoamericana (2006)

- Volume: 22, Issue: 3, page 833-849
- ISSN: 0213-2230

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topGzyl, 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 -

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