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

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发表于 2025-3-21 18:44:00 | 显示全部楼层 |阅读模式
书目名称Geometric Modeling in Probability and Statistics
编辑Ovidiu Calin,Constantin Udrişte
视频video
概述Comprehensive treatment of probability theory from the framework of differential geometry.Well-chosen problems covering a diverse spectrum of topics.Use of hands-on software to clarify and understand
图书封面Titlebook: Geometric Modeling in Probability and Statistics;  Ovidiu Calin,Constantin Udrişte Textbook 2014 Springer International Publishing Switzerl
描述.This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields..This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to. .provide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far..
出版日期Textbook 2014
关键词Entropy; Fisher information; Informational geometry; Probability density function; Statistical manifolds
版次1
doihttps://doi.org/10.1007/978-3-319-07779-6
isbn_softcover978-3-319-38162-6
isbn_ebook978-3-319-07779-6
copyrightSpringer International Publishing Switzerland 2014
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发表于 2025-3-21 22:17:16 | 显示全部楼层
Textbook 2014accompanied by software that is able to. .provide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far..
发表于 2025-3-22 02:33:36 | 显示全部楼层
https://doi.org/10.1007/978-3-476-03356-7ack can be corrected by introducing another concept, which measures the relative entropy between two given densities. This chapter studies the Kullback–Leibler relative entropy (known also as the Kullback–Leibler divergence) between two probability densities in both discrete and continuous cases.
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https://doi.org/10.1007/978-3-663-04759-9of 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.
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Métabolisme et fonctions rénalestiable 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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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.
发表于 2025-3-23 08:38:52 | 显示全部楼层
Kullback–Leibler Relative Entropyack can be corrected by introducing another concept, which measures the relative entropy between two given densities. This chapter studies the Kullback–Leibler relative entropy (known also as the Kullback–Leibler divergence) between two probability densities in both discrete and continuous cases.
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