Author: Paolo Gibilisco
Publisher: Cambridge University Press
ISBN: 0521896193
Category : Mathematics
Languages : en
Pages : 447
Book Description
An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.
Algebraic and Geometric Methods in Statistics
Author: Paolo Gibilisco
Publisher: Cambridge University Press
ISBN: 0521896193
Category : Mathematics
Languages : en
Pages : 447
Book Description
An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.
Publisher: Cambridge University Press
ISBN: 0521896193
Category : Mathematics
Languages : en
Pages : 447
Book Description
An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.
Algebraic Methods in Statistics and Probability II
Author: Marlos A. G. Viana
Publisher: American Mathematical Soc.
ISBN: 0821848917
Category : Mathematics
Languages : en
Pages : 358
Book Description
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. --
Publisher: American Mathematical Soc.
ISBN: 0821848917
Category : Mathematics
Languages : en
Pages : 358
Book Description
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 Methods in Statistics and Probability
Author: Marlos A. G. Viana
Publisher: American Mathematical Soc.
ISBN: 0821826875
Category : Mathematics
Languages : en
Pages : 354
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 0821826875
Category : Mathematics
Languages : en
Pages : 354
Book Description
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.
Algebraic Statistics
Author: Seth Sullivant
Publisher: American Mathematical Soc.
ISBN: 1470435179
Category : Education
Languages : en
Pages : 506
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 1470435179
Category : Education
Languages : en
Pages : 506
Book Description
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 for Computational Biology
Author: L. Pachter
Publisher: Cambridge University Press
ISBN: 9780521857000
Category : Mathematics
Languages : en
Pages : 440
Book Description
This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.
Publisher: Cambridge University Press
ISBN: 9780521857000
Category : Mathematics
Languages : en
Pages : 440
Book Description
This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.
Lectures on Algebraic Statistics
Author: Mathias Drton
Publisher: Springer Science & Business Media
ISBN: 3764389052
Category : Mathematics
Languages : en
Pages : 177
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 3764389052
Category : Mathematics
Languages : en
Pages : 177
Book Description
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
Author:
Publisher: American Mathematical Soc.
ISBN: 9780821856239
Category : Algebra
Languages : en
Pages : 340
Book Description
Publisher: American Mathematical Soc.
ISBN: 9780821856239
Category : Algebra
Languages : en
Pages : 340
Book Description
Methods of Mathematics Applied to Calculus, Probability, and Statistics
Author: Richard W. Hamming
Publisher: Courier Corporation
ISBN: 0486138879
Category : Mathematics
Languages : en
Pages : 882
Book Description
This 4-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. 1985 edition. Includes 310 figures and 18 tables.
Publisher: Courier Corporation
ISBN: 0486138879
Category : Mathematics
Languages : en
Pages : 882
Book Description
This 4-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. 1985 edition. Includes 310 figures and 18 tables.
Linear Algebra and Matrix Analysis for Statistics
Author: Sudipto Banerjee
Publisher: CRC Press
ISBN: 1420095382
Category : Mathematics
Languages : en
Pages : 586
Book Description
Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.
Publisher: CRC Press
ISBN: 1420095382
Category : Mathematics
Languages : en
Pages : 586
Book Description
Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.
Algebraic Geometry and Statistical Learning Theory
Author: Sumio Watanabe
Publisher: Cambridge University Press
ISBN: 0521864674
Category : Computers
Languages : en
Pages : 295
Book Description
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.
Publisher: Cambridge University Press
ISBN: 0521864674
Category : Computers
Languages : en
Pages : 295
Book Description
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.