Titlebook: Information Geometry; Nihat Ay,Jürgen Jost,Lorenz Schwachh?fer Book 2017 Springer International Publishing AG 2017 60A10, 62B05, 62B10, 62

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Finite Information Geometry,es the characteristic properties of the Fisher and Amari–Chentsov tensors for finite sample spaces, setting the stage for corresponding results for general sample spaces in subsequent chapters. It also introduces divergences and exponential and mixture families of probability distributions and descr

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The Intrinsic Geometry of Statistical Models,d a pair of torsion free connections that are dual w.r.t. .. Such a structure is equivalently given in terms of a metric tensor . and a 3-symmetric tensor ., a . in the sense of Lauritzen. We close the circle with Lê’s embedding theorem that says that any such (not necessarily) compact statistical m

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Introduction,ular probability measure that best fits that sampling distribution, and the surprisingly rich and useful geometric structure underlying this. The latter is the topic of this book. A basic geometry quantity, the Fisher metric, a 2-tensor, measures how sensitively the distributions depend on the sampl

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Finite Information Geometry,wo complementary ways to view a probability distribution. One consists in viewing it as (positive) measure with total mass 1. The other considers it as an equivalence class of such measures, determined up to a global scaling factor. The natural geometry underlying the first is that of the unit simpl

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