An Introduction to Algebraic Statistics with Tensors
Authors: Bocci, Cristiano, Chiantini, Luca
Free Preview- Introduces a setting in which problems of Algebraic Statistics have a natural translation in terms of tensor analysis
- Includes a self-contained manual of Algebraic Geometry for the study of spaces of tensors
- Contains a description of relations between Algebraic Geometry and Multilinear Algebra
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- About this Textbook
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This book provides an introduction to various aspects of Algebraic Statistics with the principal aim of supporting Master’s and PhD students who wish to explore the algebraic point of view regarding recent developments in Statistics. The focus is on the background needed to explore the connections among discrete random variables. The main objects that encode these relations are multilinear matrices, i.e., tensors. The book aims to settle the basis of the correspondence between properties of tensors and their translation in Algebraic Geometry. It is divided into three parts, on Algebraic Statistics, Multilinear Algebra, and Algebraic Geometry. The primary purpose is to describe a bridge between the three theories, so that results and problems in one theory find a natural translation to the others. This task requires, from the statistical point of view, a rather unusual, but algebraically natural, presentation of random variables and their main classical features. The third part of the book can be considered as a short, almost self-contained, introduction to the basic concepts of algebraic varieties, which are part of the fundamental background for all who work in Algebraic Statistics.
- About the authors
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Prof. Luca Chiantini is Full Professor of Geometry at the University of Siena (Italy). His research interests focus mainly on Algebraic Geometry and Multilinear Algebra, and include the theory of vector bundles on varieties and the study of secant spaces, which are the geometric counterpart of the theory of tensor ranks. In particular, he recently studied the relations between Multilinear Algebra and the theory of finite sets in projective spaces.
Prof. Cristiano Bocci is Assistant Professor of Geometry at the University of Siena (Italy). His research concerns Algebraic Geometry, Commutative Algebra, and their applications. In particular, his current interests are focused on symbolic powers of ideals, Hadamard product of varieties, and the study of secant spaces. He also works in two interdisciplinary teams in the fields of Electronic Measurements and Sound Synthesis.
- Table of contents (13 chapters)
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Systems of Random Variables and Distributions
Pages 3-13
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Basic Statistics
Pages 15-34
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Statistical Models
Pages 35-45
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Complex Projective Algebraic Statistics
Pages 47-53
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Conditional Independence
Pages 55-77
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Table of contents (13 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- An Introduction to Algebraic Statistics with Tensors
- Authors
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- Cristiano Bocci
- Luca Chiantini
- Series Title
- La Matematica per il 3+2
- Series Volume
- 118
- Copyright
- 2019
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-24624-2
- DOI
- 10.1007/978-3-030-24624-2
- Softcover ISBN
- 978-3-030-24623-5
- Series ISSN
- 2038-5722
- Edition Number
- 1
- Number of Pages
- XIX, 235
- Number of Illustrations
- 65 b/w illustrations
- Topics
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