Overview
- 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
Part of the book series: UNITEXT (UNITEXT, volume 118)
Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
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.
Similar content being viewed by others
Keywords
Table of contents (13 chapters)
-
Front Matter
-
Algebraic Statistics
-
Front Matter
-
-
Multi-linear Algebra
-
Front Matter
-
-
Commutative Algebra and Algebraic Geometry
-
Front Matter
-
-
Back Matter
Reviews
“The book under review contributes to the literature in algebraic statistics by highlighting the role of tensors, which are a vital tool in algebraic statistical theory and methods.” (Carlos Amendola, Mathematical Reviews, December, 2020)
Authors and Affiliations
About the authors
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.
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.
Bibliographic Information
Book Title: An Introduction to Algebraic Statistics with Tensors
Authors: Cristiano Bocci, Luca Chiantini
Series Title: UNITEXT
DOI: https://doi.org/10.1007/978-3-030-24624-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-24623-5Published: 17 September 2019
eBook ISBN: 978-3-030-24624-2Published: 11 September 2019
Series ISSN: 2038-5714
Series E-ISSN: 2532-3318
Edition Number: 1
Number of Pages: XIX, 235
Number of Illustrations: 65 b/w illustrations
Topics: Statistical Theory and Methods, Applications of Mathematics, Algebraic Geometry