Numerical Analysis for Statisticians

Every advance in computer architecture and software tempts statisticians to tackle numerically harder problems. To do so intelligently requires a good working knowledge of numerical analysis. This book equips students to craft their own software and to understand the advantages and disadvantages of different numerical methods. Issues of numerical stability, accurate approximation, computational complexity, and mathematical modeling share the limelight in a broad yet rigorous overview of those parts of numerical analysis most relevant to statisticians.In this second edition, the material on optimization has been completely rewritten. There is now an entire chapter on the MM algorithm in addition to more comprehensive treatments of constrained optimization, penalty and barrier methods, and model selection via the lasso. There is also new material on the Cholesky decomposition, Gram-Schmidt orthogonalization, the QR decomposition, the singular value decomposition, and reproducing kernel Hilbert spaces. The discussions of the bootstrap, permutation testing, independent Monte Carlo, and hidden Markov chains are updated, and a new chapter on advanced MCMC topics introduces students to Markov random fields, reversible jump MCMC, and convergence analysis in Gibbssampling.Numerical Analysis for Statisticians can serve as a graduate text for a course surveying computational statistics. With a careful selection of topics and appropriate supplementation, it can be used at the undergraduate level. It contains enough material for a graduate course on optimization theory. Because many chapters are nearly self-contained, professional statisticians will also find the book useful as a reference.

List of contents

Recurrence Relations.- Power Series Expansions.- Continued Fraction Expansions.- Asymptotic Expansions.- Solution of Nonlinear Equations.- Vector and Matrix Norms.- Linear Regression and Matrix Inversion.- Eigenvalues and Eigenvectors.- Singular Value Decomposition.- Splines.- Optimization Theory.- The MM Algorithm.- The EM Algorithm.- Newton s Method and Scoring.- Local and Global Convergence.- Advanced Optimization Topics.- Concrete Hilbert Spaces.- Quadrature Methods.- The Fourier Transform.- The Finite Fourier Transform.- Wavelets.- Generating Random Deviates.- Independent Monte Carlo.- Permutation Tests and the Bootstrap.- Finite-State Markov Chains.- Markov Chain Monte Carlo.- Advanced Topics in MCMC.

Summary

Every advance in computer architecture and software tempts statisticians to tackle numerically harder problems. To do so intelligently requires a good working knowledge of numerical analysis. This book equips students to craft their own software and to understand the advantages and disadvantages of different numerical methods. Issues of numerical stability, accurate approximation, computational complexity, and mathematical modeling share the limelight in a broad yet rigorous overview of those parts of numerical analysis most relevant to statisticians.
In this second edition, the material on optimization has been completely rewritten. There is now an entire chapter on the MM algorithm in addition to more comprehensive treatments of constrained optimization, penalty and barrier methods, and model selection via the lasso. There is also new material on the Cholesky decomposition, Gram-Schmidt orthogonalization, the QR decomposition, the singular value decomposition, and reproducing kernel Hilbert spaces. The discussions of the bootstrap, permutation testing, independent Monte Carlo, and hidden Markov chains are updated, and a new chapter on advanced MCMC topics introduces students to Markov random fields, reversible jump MCMC, and convergence analysis in Gibbs
sampling.
Numerical Analysis for Statisticians can serve as a graduate text for a course surveying computational statistics. With a careful selection of topics and appropriate supplementation, it can be used at the undergraduate level. It contains enough material for a graduate course on optimization theory. Because many chapters are nearly self-contained, professional statisticians will also find the book useful as a reference.

Additional text

From the reviews:
"This book provides reasonably good coverage of numerical methods that are important in statistical applications. ...but overall the text serves as a good introduction to computational statistics." - MATHEMATICAL REVIEWS
From the reviews of the second edition:
“The theory and equations are well defined and easy enough to read. … This book gives you all the details you need for choosing formulas and libraries when implementing Fourier Transforms. … this is a good book … .” (Cats and Dogs with Data, maryannedata.wordpress.com, July, 2013)
“The aim and scope of this edition is to provide upper level undergraduate students, graduate students and even researchers the understanding and working knowledge of different numerical methods. … The book is organized sequentially and is well structured. … The book can be served as a textbook and equally as a reference book. … the book will appeal to a broad interdisciplinary research community. It can also successfully be used as a reference book for practitioners, providing concrete examples, data and exercises of statistical applications.” (Technometrics, Vol. 53 (2), May, 2011)
“This is a comprehensive handbook for anyone with an interest in computational statistics, such as instructors, statisticians, modelers, data mining analysts, and software designers. For a reader with good working knowledge of numerical analysis, the book is useful for understanding the advantages and disadvantages of different numerical methods. … also suitable for students interested in refining their knowledge: a list of problems with gradually increasing difficulty is available, in addition to a list of very carefully chosen references (a real support for the reader).” (Dragos Calitoiu, Mathematical Reviews, Issue 2011 g)
“Numerical Analysis for Statisticians is a wonderful book. It provides most of the necessary background in calculusand enough algebra to conduct rigorous numerical analyses of statistical problems. … I simply enjoyed Numerical Analysis for Statisticians from beginning until end. … Numerical Analysis for Statisticians also is recommended for more senior researchers, and not only for building one or two courses on the bases of statistical computing. … an essential book to hand to graduate students as soon as they enter a statistics program.” (Christian Robert, Chance, Vol. 24 (4), 2011) 

Report

From the reviews:
"This book provides reasonably good coverage of numerical methods that are important in statistical applications. ...but overall the text serves as a good introduction to computational statistics." - MATHEMATICAL REVIEWS
From the reviews of the second edition:
"The theory and equations are well defined and easy enough to read. ... This book gives you all the details you need for choosing formulas and libraries when implementing Fourier Transforms. ... this is a good book ... ." (Cats and Dogs with Data, maryannedata.wordpress.com, July, 2013)
"The aim and scope of this edition is to provide upper level undergraduate students, graduate students and even researchers the understanding and working knowledge of different numerical methods. ... The book is organized sequentially and is well structured. ... The book can be served as a textbook and equally as a reference book. ... the book will appeal to a broad interdisciplinary research community. It can also successfully be used as a reference book for practitioners, providing concrete examples, data and exercises of statistical applications." (Technometrics, Vol. 53 (2), May, 2011)
"This is a comprehensive handbook for anyone with an interest in computational statistics, such as instructors, statisticians, modelers, data mining analysts, and software designers. For a reader with good working knowledge of numerical analysis, the book is useful for understanding the advantages and disadvantages of different numerical methods. ... also suitable for students interested in refining their knowledge: a list of problems with gradually increasing difficulty is available, in addition to a list of very carefully chosen references (a real support for the reader)." (Dragos Calitoiu, Mathematical Reviews, Issue 2011 g)
"Numerical Analysis for Statisticians is a wonderful book. It provides most of the necessary background in calculusand enough algebra to conduct rigorous numerical analyses of statistical problems. ... I simply enjoyed Numerical Analysis for Statisticians from beginning until end. ... Numerical Analysis for Statisticians also is recommended for more senior researchers, and not only for building one or two courses on the bases of statistical computing. ... an essential book to hand to graduate students as soon as they enter a statistics program." (Christian Robert, Chance, Vol. 24 (4), 2011)

Product details

• Authors: Kenneth Lange
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 25.07.2012
• EAN: 9781461426127
• ISBN: 978-1-4614-2612-7
• No. of pages: 600
• Dimensions: 179 mm x 236 mm x 33 mm
• Weight: 944 g
• Illustrations: XX, 600 p.
• Series: Statistics and Computing; Statistics and Computing
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Social sciences, law, business > Business > Economics; A, Statistics, Mathematics and Statistics, Statistics and Computing, Probability Theory and Stochastic Processes, Management science, Probability & statistics, Statistics and Computing/Statistics Programs, Mathematical & statistical software, Probabilities, Stochastics, Probability Theory, Quantitative Economics, Econometrics