Markov Bases In Algebraic Statistics

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Markov Bases in Algebraic Statistics

Satoshi Aoki,Hisayuki Hara,Akimichi Takemura
Markov Bases in Algebraic Statistics Book PDF

Author : Satoshi Aoki,Hisayuki Hara,Akimichi Takemura
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 43,6 Mb
Release : 2012-07-25
Category : Mathematics
ISBN : 9781461437192

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Markov Bases in Algebraic Statistics by Satoshi Aoki,Hisayuki Hara,Akimichi Takemura Pdf

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.

Algebraic Statistics

Seth Sullivant
Algebraic Statistics Book PDF

Author : Seth Sullivant
Publisher : American Mathematical Society
Page : 506 pages
File Size : 53,9 Mb
Release : 2023-11-17
Category : Mathematics
ISBN : 9781470475109

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Algebraic Statistics by Seth Sullivant Pdf

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.

Lectures on Algebraic Statistics

Mathias Drton,Bernd Sturmfels,Seth Sullivant
Lectures on Algebraic Statistics Book PDF

Author : Mathias Drton,Bernd Sturmfels,Seth Sullivant
Publisher : Springer Science & Business Media
Page : 172 pages
File Size : 42,8 Mb
Release : 2009-04-25
Category : Mathematics
ISBN : 9783764389055

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Lectures on Algebraic Statistics by Mathias Drton,Bernd Sturmfels,Seth Sullivant Pdf

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.

Algebraic Methods in Statistics and Probability II

Marlos A. G. Viana
Algebraic Methods in Statistics and Probability II Book PDF

Author : Marlos A. G. Viana
Publisher : American Mathematical Soc.
Page : 358 pages
File Size : 49,8 Mb
Release : 2010
Category : Algebra
ISBN : 9780821848913

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Algebraic Methods in Statistics and Probability II by Marlos A. G. Viana Pdf

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. --

Algebraic and Geometric Methods in Statistics

Paolo Gibilisco
Algebraic and Geometric Methods in Statistics Book PDF

Author : Paolo Gibilisco
Publisher : Cambridge University Press
Page : 447 pages
File Size : 41,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780521896191

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Algebraic and Geometric Methods in Statistics by Paolo Gibilisco Pdf

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

Algebraic Statistics for Computational Biology

L. Pachter,B. Sturmfels
Algebraic Statistics for Computational Biology Book PDF

Author : L. Pachter,B. Sturmfels
Publisher : Cambridge University Press
Page : 440 pages
File Size : 44,9 Mb
Release : 2005-08-22
Category : Mathematics
ISBN : 0521857007

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Algebraic Statistics for Computational Biology by L. Pachter,B. Sturmfels Pdf

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

Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers

Kenji Iohara,Philippe Malbos,Masa-Hiko Saito,Nobuki Takayama
Two Algebraic Byways from Differential Equations Gr bner Bases and Quivers Book PDF

Author : Kenji Iohara,Philippe Malbos,Masa-Hiko Saito,Nobuki Takayama
Publisher : Springer Nature
Page : 375 pages
File Size : 41,8 Mb
Release : 2020-02-20
Category : Mathematics
ISBN : 9783030264543

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Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers by Kenji Iohara,Philippe Malbos,Masa-Hiko Saito,Nobuki Takayama Pdf

This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types. Although the theory of Gröbner bases was developed in the second half of the 20th century, many works on computational methods in algebra were published well before the introduction of the modern algebraic language. Since then, new algorithms have been developed and the theory itself has greatly expanded. In comparison, diagrammatic methods in representation theory are relatively new, with the quiver varieties only being introduced – with big impact – in the 1990s. Divided into two parts, the book first discusses the theory of Gröbner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Gröbner bases to analysis on systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. It then introduces representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line. While no particular reader background is assumed, the book is intended for graduate students in mathematics, engineering and related fields, as well as researchers and scholars.

An Introduction to Algebraic Statistics with Tensors

Cristiano Bocci,Luca Chiantini
An Introduction to Algebraic Statistics with Tensors Book PDF

Author : Cristiano Bocci,Luca Chiantini
Publisher : Springer Nature
Page : 235 pages
File Size : 46,5 Mb
Release : 2019-09-11
Category : Mathematics
ISBN : 9783030246242

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An Introduction to Algebraic Statistics with Tensors by Cristiano Bocci,Luca Chiantini Pdf

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.

Algebraic and Geometric Methods in Discrete Mathematics

Heather A. Harrington,Mohamed Omar,Matthew Wright
Algebraic and Geometric Methods in Discrete Mathematics Book PDF

Author : Heather A. Harrington,Mohamed Omar,Matthew Wright
Publisher : American Mathematical Soc.
Page : 277 pages
File Size : 44,7 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

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Algebraic and Geometric Methods in Discrete Mathematics by Heather A. Harrington,Mohamed Omar,Matthew Wright Pdf

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.

Algebraic Statistics

Giovanni Pistone,Eva Riccomagno,Henry P. Wynn
Algebraic Statistics Book PDF

Author : Giovanni Pistone,Eva Riccomagno,Henry P. Wynn
Publisher : CRC Press
Page : 194 pages
File Size : 40,6 Mb
Release : 2000-12-21
Category : Mathematics
ISBN : 1420035762

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Algebraic Statistics by Giovanni Pistone,Eva Riccomagno,Henry P. Wynn Pdf

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

Gröbner Bases

Takayuki Hibi
Gr bner Bases Book PDF

Author : Takayuki Hibi
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 50,7 Mb
Release : 2014-01-07
Category : Mathematics
ISBN : 9784431545743

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Gröbner Bases by Takayuki Hibi Pdf

The idea of the Gröbner basis first appeared in a 1927 paper by F. S. Macaulay, who succeeded in creating a combinatorial characterization of the Hilbert functions of homogeneous ideals of the polynomial ring. Later, the modern definition of the Gröbner basis was independently introduced by Heisuke Hironaka in 1964 and Bruno Buchberger in 1965. However, after the discovery of the notion of the Gröbner basis by Hironaka and Buchberger, it was not actively pursued for 20 years. A breakthrough was made in the mid-1980s by David Bayer and Michael Stillman, who created the Macaulay computer algebra system with the help of the Gröbner basis. Since then, rapid development on the Gröbner basis has been achieved by many researchers, including Bernd Sturmfels. This book serves as a standard bible of the Gröbner basis, for which the harmony of theory, application, and computation are indispensable. It provides all the fundamentals for graduate students to learn the ABC’s of the Gröbner basis, requiring no special knowledge to understand those basic points. Starting from the introductory performance of the Gröbner basis (Chapter 1), a trip around mathematical software follows (Chapter 2). Then comes a deep discussion of how to compute the Gröbner basis (Chapter 3). These three chapters may be regarded as the first act of a mathematical play. The second act opens with topics on algebraic statistics (Chapter 4), a fascinating research area where the Gröbner basis of a toric ideal is a fundamental tool of the Markov chain Monte Carlo method. Moreover, the Gröbner basis of a toric ideal has had a great influence on the study of convex polytopes (Chapter 5). In addition, the Gröbner basis of the ring of differential operators gives effective algorithms on holonomic functions (Chapter 6). The third act (Chapter 7) is a collection of concrete examples and problems for Chapters 4, 5 and 6 emphasizing computation by using various software systems.

Statistics in the Public Interest

Alicia L. Carriquiry,Judith M. Tanur,William F. Eddy
Statistics in the Public Interest Book PDF

Author : Alicia L. Carriquiry,Judith M. Tanur,William F. Eddy
Publisher : Springer Nature
Page : 574 pages
File Size : 53,5 Mb
Release : 2022-04-22
Category : Mathematics
ISBN : 9783030754600

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Statistics in the Public Interest by Alicia L. Carriquiry,Judith M. Tanur,William F. Eddy Pdf

This edited volume surveys a variety of topics in statistics and the social sciences in memory of the late Stephen Fienberg. The book collects submissions from a wide range of contemporary authors to explore the fields in which Fienberg made significant contributions, including contingency tables and log-linear models, privacy and confidentiality, forensics and the law, the decennial census and other surveys, the National Academies, Bayesian theory and methods, causal inference and causes of effects, mixed membership models, and computing and machine learning. Each section begins with an overview of Fienberg’s contributions and continues with chapters by Fienberg’s students, colleagues, and collaborators exploring recent advances and the current state of research on the topic. In addition, this volume includes a biographical introduction as well as a memorial concluding chapter comprised of entries from Stephen and Joyce Fienberg’s close friends, former students, colleagues, and other loved ones, as well as a photographic tribute.

Nonparametric Statistics

Michele La Rocca,Brunero Liseo,Luigi Salmaso
Nonparametric Statistics Book PDF

Author : Michele La Rocca,Brunero Liseo,Luigi Salmaso
Publisher : Springer Nature
Page : 547 pages
File Size : 49,9 Mb
Release : 2020-11-11
Category : Mathematics
ISBN : 9783030573065

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Nonparametric Statistics by Michele La Rocca,Brunero Liseo,Luigi Salmaso Pdf

Highlighting the latest advances in nonparametric and semiparametric statistics, this book gathers selected peer-reviewed contributions presented at the 4th Conference of the International Society for Nonparametric Statistics (ISNPS), held in Salerno, Italy, on June 11-15, 2018. It covers theory, methodology, applications and computational aspects, addressing topics such as nonparametric curve estimation, regression smoothing, models for time series and more generally dependent data, varying coefficient models, symmetry testing, robust estimation, and rank-based methods for factorial design. It also discusses nonparametric and permutation solutions for several different types of data, including ordinal data, spatial data, survival data and the joint modeling of both longitudinal and time-to-event data, permutation and resampling techniques, and practical applications of nonparametric statistics. The International Society for Nonparametric Statistics is a unique global organization, and its international conferences are intended to foster the exchange of ideas and the latest advances and trends among researchers from around the world and to develop and disseminate nonparametric statistics knowledge. The ISNPS 2018 conference in Salerno was organized with the support of the American Statistical Association, the Institute of Mathematical Statistics, the Bernoulli Society for Mathematical Statistics and Probability, the Journal of Nonparametric Statistics and the University of Salerno.

Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics

Shuhei Mano
Partitions Hypergeometric Systems and Dirichlet Processes in Statistics Book PDF

Author : Shuhei Mano
Publisher : Springer
Page : 135 pages
File Size : 49,5 Mb
Release : 2018-07-12
Category : Mathematics
ISBN : 9784431558880

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Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics by Shuhei Mano Pdf

This book focuses on statistical inferences related to various combinatorial stochastic processes. Specifically, it discusses the intersection of three subjects that are generally studied independently of each other: partitions, hypergeometric systems, and Dirichlet processes. The Gibbs partition is a family of measures on integer partition, and several prior processes, such as the Dirichlet process, naturally appear in connection with infinite exchangeable Gibbs partitions. Examples include the distribution on a contingency table with fixed marginal sums and the conditional distribution of Gibbs partition given the length. The A-hypergeometric distribution is a class of discrete exponential families and appears as the conditional distribution of a multinomial sample from log-affine models. The normalizing constant is the A-hypergeometric polynomial, which is a solution of a system of linear differential equations of multiple variables determined by a matrix A, called A-hypergeometric system. The book presents inference methods based on the algebraic nature of the A-hypergeometric system, and introduces the holonomic gradient methods, which numerically solve holonomic systems without combinatorial enumeration, to compute the normalizing constant. Furher, it discusses Markov chain Monte Carlo and direct samplers from A-hypergeometric distribution, as well as the maximum likelihood estimation of the A-hypergeometric distribution of two-row matrix using properties of polytopes and information geometry. The topics discussed are simple problems, but the interdisciplinary approach of this book appeals to a wide audience with an interest in statistical inference on combinatorial stochastic processes, including statisticians who are developing statistical theories and methodologies, mathematicians wanting to discover applications of their theoretical results, and researchers working in various fields of data sciences.

Looking Back

Neil J. Dorans,Sandip Sinharay
Looking Back Book PDF

Author : Neil J. Dorans,Sandip Sinharay
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 53,9 Mb
Release : 2011-07-15
Category : Social Science
ISBN : 9781441993892

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Looking Back by Neil J. Dorans,Sandip Sinharay Pdf

In 2006, Paul W. Holland retired from Educational Testing Service (ETS) after a career spanning five decades. In 2008, ETS sponsored a conference, Looking Back, honoring his contributions to applied and theoretical psychometrics and statistics. Looking Back attracted a large audience that came to pay homage to Paul Holland and to hear presentations by colleagues who worked with him in special ways over those 40+ years. This book contains papers based on these presentations, as well as vignettes provided by Paul Holland before each section. The papers in this book attest to how Paul Holland's pioneering ideas influenced and continue to influence several fields such as social networks, causal inference, item response theory, equating, and DIF. He applied statistical thinking to a broad range of ETS activities in test development, statistical analysis, test security, and operations. The original papers contained in this book provide historical context for Paul Holland’s work alongside commentary on some of his major contributions by noteworthy statisticians working today.