An Introduction to Algebraic Statistics with Tensors - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Algebraic Statistics with Tensors write by Cristiano Bocci. This book was released on 2019-09-11. An Introduction to Algebraic Statistics with Tensors available in PDF, EPUB and Kindle. 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.
Tensors: Geometry and Applications
Tensors: Geometry and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Tensors: Geometry and Applications write by J. M. Landsberg. This book was released on 2011-12-14. Tensors: Geometry and Applications available in PDF, EPUB and Kindle. Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.
Tensor Methods in Statistics
Tensor Methods in Statistics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Tensor Methods in Statistics write by Peter McCullagh. This book was released on 2018-07-18. Tensor Methods in Statistics available in PDF, EPUB and Kindle. A pioneering monograph on tensor methods applied to distributional problems arising in statistics, this work begins with the study of multivariate moments and cumulants. An invaluable reference for graduate students and professional statisticians. 1987 edition.
Introduction to Tensor Analysis and the Calculus of Moving Surfaces
Introduction to Tensor Analysis and the Calculus of Moving Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Tensor Analysis and the Calculus of Moving Surfaces write by Pavel Grinfeld. This book was released on 2013-09-24. Introduction to Tensor Analysis and the Calculus of Moving Surfaces available in PDF, EPUB and Kindle. This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.
Algebraic Statistics for Computational Biology
Algebraic Statistics for Computational Biology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Statistics for Computational Biology write by L. Pachter. This book was released on 2005-08-22. Algebraic Statistics for Computational Biology available in PDF, EPUB and Kindle. This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.
