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Author : Paolo Gibilisco
Publisher : Cambridge University Press
Page : 447 pages
File Size : 40,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780521896191
An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.
Author : Fedor Bogomolov,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 365 pages
File Size : 49,6 Mb
Release : 2006-06-22
Category : Mathematics
ISBN : 9780817644178
* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry
Author : Shun-ichi Amari
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461250562
From the reviews: "In this Lecture Note volume the author describes his differential-geometric approach to parametrical statistical problems summarizing the results he had published in a series of papers in the last five years. The author provides a geometric framework for a special class of test and estimation procedures for curved exponential families. ... ... The material and ideas presented in this volume are important and it is recommended to everybody interested in the connection between statistics and geometry ..." #Metrika#1 "More than hundred references are given showing the growing interest in differential geometry with respect to statistics. The book can only strongly be recommended to a geodesist since it offers many new insights into statistics on a familiar ground." #Manuscripta Geodaetica#2
Author : Mathias Drton,Bernd Sturmfels,Seth Sullivant
Publisher : Springer Science & Business Media
Page : 172 pages
File Size : 46,8 Mb
Release : 2009-04-25
Category : Mathematics
ISBN : 9783764389055
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 : Heather A. Harrington,Mohamed Omar,Matthew Wright
Publisher : American Mathematical Soc.
Page : 277 pages
File Size : 49,6 Mb
Release : 2017-03-16
Category : Commutative algebra -- Computational aspects and applications -- Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
ISBN : 9781470423216
This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Methods in Applied Discrete Mathematics, held on January 11, 2015, in San Antonio, Texas. The papers present connections between techniques from “pure” mathematics and various applications amenable to the analysis of discrete models, encompassing applications of combinatorics, topology, algebra, geometry, optimization, and representation theory. Papers not only present novel results, but also survey the current state of knowledge of important topics in applied discrete mathematics. Particular highlights include: a new computational framework, based on geometric combinatorics, for structure prediction from RNA sequences; a new method for approximating the optimal solution of a sum of squares problem; a survey of recent Helly-type geometric theorems; applications of representation theory to voting theory and game theory; a study of fixed points of tensors; and exponential random graph models from the perspective of algebraic statistics with applications to networks. This volume was written for those trained in areas such as algebra, topology, geometry, and combinatorics who are interested in tackling problems in fields such as biology, the social sciences, data analysis, and optimization. It may be useful not only for experts, but also for students who wish to gain an applied or interdisciplinary perspective.
Author : Cristiano Bocci,Luca Chiantini
Publisher : Springer Nature
Page : 235 pages
File Size : 42,5 Mb
Release : 2019-09-11
Category : Mathematics
ISBN : 9783030246242
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 : Michael Joswig,Thorsten Theobald
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 49,5 Mb
Release : 2013-01-04
Category : Mathematics
ISBN : 9781447148173
Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.
Author : Peter Falb
Publisher : Springer
Page : 202 pages
File Size : 55,7 Mb
Release : 2018-08-25
Category : Mathematics
ISBN : 9783319980263
"An introduction to the ideas of algebraic geometry in the motivated context of system theory." Thus the author describes his textbook that has been specifically written to serve the needs of students of systems and control. Without sacrificing mathematical care, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than abstraction. The student will find here a clear presentation with an applied flavor, of the core ideas in the algebra-geometric treatment of scalar linear system theory. The author introduces the four representations of a scalar linear system and establishes the major results of a similar theory for multivariable systems appearing in a succeeding volume (Part II: Multivariable Linear Systems and Projective Algebraic Geometry). Prerequisites are the basics of linear algebra, some simple notions from topology and the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises are an integral part of the treatment and are used where relevant in the main body of the text. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "This book is a concise development of affine algebraic geometry together with very explicit links to the applications...[and] should address a wide community of readers, among pure and applied mathematicians." —Monatshefte für Mathematik
Author : Sumio Watanabe
Publisher : Cambridge University Press
Page : 295 pages
File Size : 40,5 Mb
Release : 2009-08-13
Category : Computers
ISBN : 9780521864671
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 : Seth Sullivant
Publisher : American Mathematical Society
Page : 506 pages
File Size : 48,6 Mb
Release : 2023-11-17
Category : Mathematics
ISBN : 9781470475109
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 : David J. Saville,Graham R. Wood
Publisher : CreateSpace
Page : 280 pages
File Size : 52,9 Mb
Release : 2011-03-20
Category : Science
ISBN : 1456420429
Are you an applied researcher or a statistics student? If so, have you ever wondered if there is any rhyme or reason behind the apparent jumble of ad hoc statistical “recipes” that are most commonly used by researchers? If you have, then this book is for you! Within its pages, the rhyme and reason are explained in a surprisingly simple, visual and appealing manner. The statistical methods referred to are those based on the “Normal” distribution. They include the paired and independent samples t tests, analysis of variance, and regression. The rhyme is explained by analysing four case studies, one for each of these topics. The key to the rhyme is to use elementary vector geometry. Then the crucial ideas are easily explained by drawing right-angled triangles and applying Pythagoras' Theorem. “Keep it simple” has been our aim. The geometric ideas are first introduced and applied to data sets in two and three dimensions, before we gently introduce higher dimensional examples. Throughout, we use real data sets taken from real research studies, and take care to explain the interpretation of the statistical analyses. In this way, the book integrates the algebraic, numeric, geometric and practical aspects of these basic statistical methods.We hope that many students as well as practicing researchers and statisticians will enjoy this novel visual approach to these ideas.
Author : Marlos A. G. Viana
Publisher : American Mathematical Soc.
Page : 358 pages
File Size : 40,7 Mb
Release : 2010
Category : Algebra
ISBN : 9780821848913
A decade after the publication of Contemporary Mathematics Vol. 287, the present volume demonstrates the consolidation of important areas, such as algebraic statistics, computational commutative algebra, and deeper aspects of graphical models. --
Author : L. Pachter,B. Sturmfels
Publisher : Cambridge University Press
Page : 440 pages
File Size : 48,8 Mb
Release : 2005-08-22
Category : Mathematics
ISBN : 0521857007
This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.
Author : Marlos A. G. Viana,Ams Special Session on Algebraic Methods in Statistics,Donald St. P. Richards
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 47,6 Mb
Release : 2001
Category : Algebra
ISBN : 9780821826874
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 : David J. Saville,Graham R. Wood
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207474
The aim of this book is to present the mathematics underlying elementary statistical methods in as simple a manner as possible. These methods include independent and paired sample t-tests, analysis of variance, regression, and the analysis of covariance. The author's principle tool is the use of geometric ideas to provide more visual insight and to make the theory accessible to a wider audience than is usually possible.
