Author : Marlos A. G. Viana
Publisher : American Mathematical Soc.
Page : 358 pages
File Size : 11,19 MB
Release : 2010
Category : Mathematics
ISBN : 0821848917
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 :
Publisher : American Mathematical Soc.
Page : 340 pages
File Size : 24,33 MB
Release : 2001
Category : Algebra
ISBN : 9780821856239
Author : Paolo Gibilisco
Publisher : Cambridge University Press
Page : 447 pages
File Size : 31,35 MB
Release : 2010
Category : Mathematics
ISBN : 0521896193
An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.
Author : Marlos A. G. Viana
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 44,44 MB
Release : 2001
Category : Mathematics
ISBN : 0821826875
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 : L. Pachter
Publisher : Cambridge University Press
Page : 440 pages
File Size : 40,14 MB
Release : 2005-08-22
Category : Mathematics
ISBN : 9780521857000
This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.
Author : Alicia L. Carriquiry
Publisher : Springer Nature
Page : 574 pages
File Size : 17,3 MB
Release : 2022-04-22
Category : Mathematics
ISBN : 303075460X
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.
Author : Vasudevan Lakshminarayanan
Publisher : CRC Press
Page : 632 pages
File Size : 32,11 MB
Release : 2012-12-14
Category : Science
ISBN : 143986960X
Going beyond standard introductory texts, Mathematical Optics: Classical, Quantum, and Computational Methods brings together many new mathematical techniques from optical science and engineering research. Profusely illustrated, the book makes the material accessible to students and newcomers to the field. Divided into six parts, the text presents state-of-the-art mathematical methods and applications in classical optics, quantum optics, and image processing. Part I describes the use of phase space concepts to characterize optical beams and the application of dynamic programming in optical waveguides. Part II explores solutions to paraxial, linear, and nonlinear wave equations. Part III discusses cutting-edge areas in transformation optics (such as invisibility cloaks) and computational plasmonics. Part IV uses Lorentz groups, dihedral group symmetry, Lie algebras, and Liouville space to analyze problems in polarization, ray optics, visual optics, and quantum optics. Part V examines the role of coherence functions in modern laser physics and explains how to apply quantum memory channel models in quantum computers. Part VI introduces super-resolution imaging and differential geometric methods in image processing. As numerical/symbolic computation is an important tool for solving numerous real-life problems in optical science, many chapters include Mathematica® code in their appendices. The software codes and notebooks as well as color versions of the book’s figures are available at www.crcpress.com.
Author : Mathias Drton
Publisher : Springer Science & Business Media
Page : 177 pages
File Size : 20,32 MB
Release : 2009-04-25
Category : Mathematics
ISBN : 3764389052
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 : Satoshi Aoki
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 39,61 MB
Release : 2012-07-25
Category : Mathematics
ISBN : 1461437199
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 : Seth Sullivant
Publisher : American Mathematical Soc.
Page : 506 pages
File Size : 31,35 MB
Release : 2018-11-19
Category : Education
ISBN : 1470435179
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.
