Algebraic Statistics
DOWNLOAD
Download Algebraic Statistics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Algebraic Statistics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Algebraic Statistics
DOWNLOAD
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 Statistics
DOWNLOAD
Author : Giovanni Pistone
language : en
Publisher: CRC Press
Release Date : 2000-12-21
Algebraic Statistics written by Giovanni Pistone and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-12-21 with Mathematics categories.
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
Markov Bases In Algebraic Statistics
DOWNLOAD
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
DOWNLOAD
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.
Algebraic Statistics For Computational Biology
DOWNLOAD
Author : L. Pachter
language : en
Publisher: Cambridge University Press
Release Date : 2005-08-22
Algebraic Statistics For Computational Biology written by L. Pachter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-22 with Mathematics categories.
This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.
An Introduction To Algebraic Statistics With Tensors
DOWNLOAD
Author : Cristiano Bocci
language : en
Publisher: Springer Nature
Release Date : 2019-09-11
An Introduction To Algebraic Statistics With Tensors written by Cristiano Bocci and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-11 with Mathematics categories.
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 Statistics
DOWNLOAD
Author : Paolo Gibilisco
language : en
Publisher: Cambridge University Press
Release Date : 2010
Algebraic And Geometric Methods In Statistics written by Paolo Gibilisco and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.
Semialgebraic Statistics And Latent Tree Models
DOWNLOAD
Author : Piotr Zwiernik
language : en
Publisher: CRC Press
Release Date : 2015-08-21
Semialgebraic Statistics And Latent Tree Models written by Piotr Zwiernik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-21 with Mathematics categories.
The first part of the book gives a general introduction to key concepts in algebraic statistics, focusing on methods that are helpful in the study of models with hidden variables. The author uses tensor geometry as a natural language to deal with multivariate probability distributions, develops new combinatorial tools to study models with hidden data, and describes the semialgebraic structure of statistical models. The second part illustrates important examples of tree models with hidden variables. The book discusses the underlying models and related combinatorial concepts of phylogenetic trees as well as the local and global geometry of latent tree models. It also extends previous results to Gaussian latent tree models. This book shows you how both combinatorics and algebraic geometry enable a better understanding of latent tree models. It contains many results on the geometry of the models, including a detailed analysis of identifiability and the defining polynomial constraints
Algebraic Statistics
DOWNLOAD
Author : Karl-Heinz Zimmermann
language : en
Publisher:
Release Date : 2015
Algebraic Statistics written by Karl-Heinz Zimmermann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
Algebraic statistics brings together ideas from algebraic geometry, commutative algebra, and combinatorics to address problems in statistics and its applications. Computer algebra provides powerful tools for the study of algorithms and software. However, these tools are rarely prepared to address statistical challenges and therefore new algebraic results need often be developed. This way of interplay between algebra and statistics fertilizes both disciplines. Algebraic statistics is a relatively new branch of mathematics that developed and changed rapidly over the last ten years. The seminal work in this field was the paper of Diaconis and Sturmfels (1998) introducing the notion of Markov bases for toric statistical models and showing the connection to commutative algebra. Later on, the connection between algebra and statistics spread to a number of different areas including parametric inference, phylogenetic invariants, and algebraic tools for maximum likelihood estimation. These connection were highlighted in the celebrated book Algebraic Statistics for Computational Biology of Pachter and Sturmfels (2005) and subsequent publications. In this report, statistical models for discrete data are viewed as solutions of systems of polynomial equations. This allows to treat statistical models for sequence alignment, hidden Markov models, and phylogenetic tree models. These models are connected in the sense that if they are interpreted in the tropical algebra, the famous dynamic programming algorithms (Needleman-Wunsch, Viterbi, and Felsenstein) occur in a natural manner. More generally, if the models are interpreted in a higher dimensional analogue of the tropical algebra, the polytope algebra, parametric versions of these dynamic programming algorithms can be established. Markov bases allow to sample data in a given fibre using Markov chain Monte Carlo algorithms. In this way, Markov bases provide a means to increase the sample size and make statistical tests in inferential statistics more reliable. We will calculate Markov bases using Groebner bases in commutative polynomial rings. The manuscript grew out of lectures on algebraic statistics held for Master students of Computer Science at the Hamburg University of Technology. It appears that the first lecture held in the summer term 2008 was the first course of this kind in Germany. The current manuscript is the basis of a four-hour introductory course. The use of computer algebra systems is at the heart of the course. Maple is employed for symbolic computations, Singular for algebraic computations, and R for statistical computations. The second edition at hand is just a streamlined version of the first one.$cen$dAbstract
Algebraic Methods In Statistics And Probability Ii
DOWNLOAD
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. --