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.

Bocci, C., Chiantini, L. (2019). An Introduction to Algebraic Statistics with Tensors. Cham : Springer [10.1007/978-3-030-24624-2].

### An Introduction to Algebraic Statistics with Tensors

#### Abstract

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.
##### Scheda breve Scheda completa Scheda completa (DC)
2019
978-3-030-24623-5
Bocci, C., Chiantini, L. (2019). An Introduction to Algebraic Statistics with Tensors. Cham : Springer [10.1007/978-3-030-24624-2].
File in questo prodotto:
File
An+Introduction+to+Algebraic+Statistics+.pdf

non disponibili

Tipologia: PDF editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 3.71 MB
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11365/1225896`