Electronic Resource

An Invitation to Statistics in Wasserstein Space

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This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph. ; Gives a succinct introduction to necessary mathematical background, focusing on the results useful for statistics from an otherwise vast mathematical literature. Presents an up to date overview of the state of the art, including some original results, and discusses open problems. Suitable for self-study or to be used as a graduate level course text. Open access.

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Detail Information

Series Title

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Call Number

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Publisher

Cham : Springer Nature., 2020

Collation

147 hlm., ill., lamp

Language

English

ISBN/ISSN

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Classification

NONE

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

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Subject(s)

Probability and statistics

Specific Detail Info

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Statement of Responsibility

Panaretos, Victor M. ; Zemel, Yoav

Other Information

Cataloger

ida

Source

https://directory.doabooks.org/handle/20.500.12854/37237

Validator

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Digital Object Identifier (DOI)

10.1007/978-3-030-38438-8

Journal Volume

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Journal Issue

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Subtitle

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Parallel Title

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