A geometry on the space of probabilities II. Projectives spaces and exponential families

• Autores: Henryk Gzyl , Lázaro Recht
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 22, Nº 3, 2006, págs. 833-850
• Idioma: inglés
• DOI: 10.4171/rmi/475
• Títulos paralelos:
  • Una geometría en el espacio de probabilidades (II).: Espacios proyectivos familias exponenciales.
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• Resumen

  • 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