Information Geometry 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Nihat Ay 作者

Springer

译者

2017-8-26 出版日期

407 页数

USD 129.00 价格

Hardcover

丛书系列

9783319564777 图书编码

Information Geometry 在线电子书图书标签: 信息论信息几何 Geometry 数学-geometry Statistics

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发表于2024-11-25

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Information Geometry 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

Information Geometry 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Information Geometry 在线电子书图书描述

The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated.

This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo.

The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems

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