ENGLISH

An Introduction to Algebraic Statistics with Tensors

By Cristiano Bocci , Luca Chiantini

Book information

Publisher
Springer International Publishing
Year
2019
ISBN
9783030246242
Language
english
Format
EPUB
Filesize
14 MB (15079800 bytes)
Series
UNITEXT - La Matematica per il 3+2, 118
Pages
256\0
Time added
2019-10-02 21:08:00

Description

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.

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