An Introduction to Algebraic Statistics with Tensors

• Main Authors: Bocci, Cristiano (Author, http://id.loc.gov/vocabulary/relators/aut), Chiantini, Luca (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: La Matematica per il 3+2, 118
• Subjects: Statistics .; Applied mathematics.; Engineering mathematics.; Algebraic geometry.; Statistical Theory and Methods.; Applications of Mathematics.; Algebraic Geometry.

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 connecti...

Table of Contents:

• 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.