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Markov Bases In Algebraic Statistics

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Markov Bases In Algebraic Statistics

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Author : Satoshi Aoki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-25

Markov Bases In Algebraic Statistics written by Satoshi Aoki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-25 with Mathematics categories.

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.

Lectures On Algebraic Statistics

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Author : Mathias Drton
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-25

Lectures On Algebraic Statistics written by Mathias Drton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-25 with Mathematics categories.

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.

Lectures On Algebraic Statistics

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Author : Mathias Drton
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10

Algebraic Statistics

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Author : Seth Sullivant
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-17

Algebraic Statistics written by Seth Sullivant and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-17 with Mathematics categories.

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.

Algebraic Methods In Statistics And Probability Ii

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Author : Marlos A. G. Viana
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Algebraic Methods In Statistics And Probability Ii written by Marlos A. G. Viana and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

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. --

Statistics In The Public Interest

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Author : Alicia L. Carriquiry
language : en
Publisher: Springer Nature
Release Date : 2022-04-22

Statistics In The Public Interest written by Alicia L. Carriquiry and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-22 with Mathematics categories.

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.

Looking Back

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Author : Neil J. Dorans
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-15

Looking Back written by Neil J. Dorans and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-15 with Social Science categories.

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.

Algebraic And Geometric Methods In Discrete Mathematics

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Author : Heather A. Harrington
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-03-16

Algebraic And Geometric Methods In Discrete Mathematics written by Heather A. Harrington and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-16 with Mathematics categories.

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.

Advanced Statistical Methods For The Analysis Of Large Data Sets

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Author : Agostino Di Ciaccio
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-03-14

Advanced Statistical Methods For The Analysis Of Large Data Sets written by Agostino Di Ciaccio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-14 with Mathematics categories.

The theme of the meeting was “Statistical Methods for the Analysis of Large Data-Sets”. In recent years there has been increasing interest in this subject; in fact a huge quantity of information is often available but standard statistical techniques are usually not well suited to managing this kind of data. The conference serves as an important meeting point for European researchers working on this topic and a number of European statistical societies participated in the organization of the event. The book includes 45 papers from a selection of the 156 papers accepted for presentation and discussed at the conference on “Advanced Statistical Methods for the Analysis of Large Data-sets.”

Two Algebraic Byways From Differential Equations Gr Bner Bases And Quivers

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Author : Kenji Iohara
language : en
Publisher: Springer Nature
Release Date : 2020-02-20

Two Algebraic Byways From Differential Equations Gr Bner Bases And Quivers written by Kenji Iohara and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-20 with Mathematics categories.

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.

Markov Bases In Algebraic Statistics

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