[PDF] Algebraic Statistics eBook

Author : Seth Sullivant
Publisher : American Mathematical Soc.
Page : 490 pages
File Size : 18,2 MB
Release : 2018-11-19
Category : Geometry, Algebraic
ISBN : 1470435179

GET BOOK

Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.

Author : Cristiano Bocci
Publisher : Springer Nature
Page : 235 pages
File Size : 26,68 MB
Release : 2019-09-11
Category : Mathematics
ISBN : 3030246248

GET BOOK

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.

Author : L. Pachter
Publisher : Cambridge University Press
Page : 440 pages
File Size : 35,24 MB
Release : 2005-08-22
Category : Mathematics
ISBN : 9780521857000

GET BOOK

This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.

Author : Giovanni Pistone
Publisher : CRC Press
Page : 180 pages
File Size : 19,19 MB
Release : 2000-12-21
Category : Mathematics
ISBN : 1420035762

GET BOOK

Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Grobner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case

Author : Mathias Drton
Publisher : Springer Science & Business Media
Page : 177 pages
File Size : 43,36 MB
Release : 2009-04-25
Category : Mathematics
ISBN : 3764389052

GET BOOK

How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.

Author : Sumio Watanabe
Publisher : Cambridge University Press
Page : 295 pages
File Size : 14,61 MB
Release : 2009-08-13
Category : Computers
ISBN : 0521864674

GET BOOK

Sure to be influential, Watanabe's book lays the foundations for the use of algebraic geometry in statistical learning theory. Many models/machines are singular: mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.

Author : Paolo Gibilisco
Publisher : Cambridge University Press
Page : 447 pages
File Size : 44,57 MB
Release : 2010
Category : Mathematics
ISBN : 0521896193

GET BOOK

An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.

Author : Satoshi Aoki
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 50,15 MB
Release : 2012-07-25
Category : Mathematics
ISBN : 1461437199

GET BOOK

Algebraic statistics is a rapidly developing field, where ideas from statistics and algebra meet and stimulate new research directions. One of the origins of algebraic statistics is the work by Diaconis and Sturmfels in 1998 on the use of Gröbner bases for constructing a connected Markov chain for performing conditional tests of a discrete exponential family. In this book we take up this topic and present a detailed summary of developments following the seminal work of Diaconis and Sturmfels. This book is intended for statisticians with minimal backgrounds in algebra. As we ourselves learned algebraic notions through working on statistical problems and collaborating with notable algebraists, we hope that this book with many practical statistical problems is useful for statisticians to start working on the field.

Author : Marlos A. G. Viana
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 15,24 MB
Release : 2001
Category : Mathematics
ISBN : 0821826875

GET BOOK

The 23 papers report recent developments in using the technique to help clarify the relationship between phenomena and data in a number of natural and social sciences. Among the topics are a coordinate-free approach to multivariate exponential families, some rank-based hypothesis tests for covariance structure and conditional independence, deconvolution density estimation on compact Lie groups, random walks on regular languages and algebraic systems of generating functions, and the extendibility of statistical models. There is no index. c. Book News Inc.

Author : Richard E. Blahut
Publisher : Cambridge University Press
Page : 10 pages
File Size : 16,66 MB
Release : 2008-04-03
Category : Technology & Engineering
ISBN : 1139469460

GET BOOK

The past few years have witnessed significant developments in algebraic coding theory. This book provides an advanced treatment of the subject from an engineering perspective, covering the basic principles and their application in communications and signal processing. Emphasis is on codes defined on the line, on the plane, and on curves, with the core ideas presented using commutative algebra and computational algebraic geometry made accessible using the Fourier transform. Starting with codes defined on a line, a background framework is established upon which the later chapters concerning codes on planes, and on curves, are developed. The decoding algorithms are developed using the standard engineering approach applied to those of Reed-Solomon codes, enabling them to be evaluated against practical applications. Integrating recent developments in the field into the classical treatment of algebraic coding, this is an invaluable resource for graduate students and researchers in telecommunications and applied mathematics.