Devastate 发表于 2025-3-26 23:10:33
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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 connBRAND 发表于 2025-3-27 10:23:40
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 发表于 2025-3-27 14:27:54
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 发表于 2025-3-27 21:36:11
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 multidimensionalDeject 发表于 2025-3-28 01:01:54
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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 发表于 2025-3-28 07:24:35
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.Transfusion 发表于 2025-3-28 10:39:01
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