A geometry on the space of probabilities. II: Projective spaces and exponential families
Summary: We continue a theme taken up in Part I, see [\textit{H.\,Gzyl} and \textit{L.\,Recht}, Rev.\ Mat.\ Iberom.\ 22, 545--558 (2006; Zbl 1121.46043)], namely, to provide a geometric interpretation of exponential families as endpoints 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 develop everything in a generic \({\mathcal C}^*\)-algebra setting, but have the function space model in mind.
scientific article; zbMATH DE number 5149120