An Introduction to Algebraic Statistics with Tensors
Buch in deiner Nähe kaufen
Beschreibung
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.
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.
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
Autor*in
Cristiano Bocci
Themen in »An Introduction to Algebraic Statistics with Tensors«
Algebraic Statistics Multilinear Algebra Tensor Analysis
Stimmen zu »An Introduction to Algebraic Statistics with Tensors«
“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)
()