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Catalogue Information
Field name	Details
Dewey Class	519.5
Title	An Introduction to Algebraic Statistics with Tensors ([EBook]) / by Cristiano Bocci, Luca Chiantini.
Author	Bocci, Cristiano
Added Personal Name	Chiantini, Luca
Other name(s)	SpringerLink (Online service)
Publication	Cham : Springer International Publishing , 2019.
Physical Details	XIX, 235 pages : 65 illus. : online resource.
Series	La Matematica per il 3+2 ; 118
ISBN	9783030246242
Summary Note	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.:
Contents note	PART I: Algebraic Statistics -- 1 Systems of Random Variables and Distributions -- 2 Basic Statistics -- 3 Statistical models -- 4 Complex projective algebraic statistics -- 5 Conditional independence -- PART II: Multilinear Algebra -- 6 Tensors -- 7 Symmetric tensors -- 8 Marginalisation and attenings -- PART III: Commutative Algebra and Algebraic Geometry -- 9 Elements of Projective Algebraic Geometry -- 10 Projective maps and the Chow's Theorem -- 11 Dimension Theory -- 12 Secant varieties -- 13 Groebner bases.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-030-24624-2
Links to Related Works	Subject References: Algebraic Geometry . Applications of Mathematics . Applied mathematics . Engineering mathematics . Statistical Theory and Methods . Statistics . Authors: author . Bocci, Cristiano . Chiantini, Luca . Corporate Authors: SpringerLink (Online service) . Series: La Matematica per il 3+2 . Classification: 519.5 . 519.5 (DDC 23) .

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An Introduction to Algebraic Statistics with Tensors

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