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• W2013233602 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 $mathcal{C}^*$-algebra setting, but shall have the function space model in mind." @default.
• W2013233602 created "2016-06-24" @default.
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• W2013233602 date "2006-01-01" @default.
• W2013233602 modified "2023-09-30" @default.
• W2013233602 title "A geometry on the space of probabilities II. Projective spaces and exponential families" @default.
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• W2013233602 doi "https://doi.org/10.4171/rmi/475" @default.
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