Titlebook: Geometric Modeling in Probability and Statistics; Ovidiu Calin,Constantin Udrişte Textbook 2014 Springer International Publishing Switzerl

Devastate

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puzzle

https://doi.org/10.33283/978-3-86298-860-0tatistical manifold or statistical model .. A contrast function, .(. | | .), for density functions ., is a smooth, non-negative function that vanishes for . = .. Eguchi [., ., .] has shown that a contrast function . induces a Riemannian metric by its second order derivatives, and a pair of dual conn

BRAND

https://doi.org/10.1007/978-3-031-69084-6ative entropy, .-divergence, Hellinger distance, Chernoff information, Jefferey distance, Kagan divergence, and exponential contrast function. The relation with the skewness tensor and .-connection is made. The goal of this chapter is to produce hands-on examples for the theoretical concepts introdu

灿烂

https://doi.org/10.1007/978-3-031-69698-5 the first and second fundamental forms, curvatures, mean curvatures, and the relations among them..This material adapts the well-known theory of submanifolds to the statistical manifolds framework and consists mainly in the contributions of the authors.

胶水

Statistical Modelsic structure. This chapter deals with statistical models given parametrically. By specifying the parameters of a distribution, we determine a unique element of the family. When the family of distributions can be described smoothly by a set of parameters, this can be considered as a multidimensional

Deject

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Maximum Entropy Distributionsof mean, variance, or any . moments. The solution of these variational problems belongs to the exponential family. However, explicit solutions exist only in a few particular cases. A distinguished role is played by the study of the Maxwell–Boltzmann distribution.

BUST

An Introduction to Manifoldstiable manifolds, tangent space, vector fields, differentiable maps, 1-forms, tensors, linear connections, Riemannian manifolds, and the Levi–Civita connection. The material of this chapter forms the basis for next chapters.

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