Overview
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.
Full Product Details
Author: Kenneth Lange
Publisher: Springer-Verlag New York Inc.
Imprint: Springer-Verlag New York Inc.
Edition: 2nd ed. 2010
Dimensions:
Width: 16.00cm
, Height: 3.30cm
, Length: 24.00cm
Weight: 2.300kg
ISBN: 9781441959447
ISBN 10: 1441959440
Pages: 600
Publication Date: 15 June 2010
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: Awaiting stock
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Reviews
From a review of the first edition: MATHEMATICAL 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.
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: ""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) ""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)
