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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. Kenneth Lange is the Rosenfeld Professor of Computational Genetics in the Departments of Biomathematics and Human Genetics and the Chair of the Department of Human Genetics, all in the UCLA School of Medicine. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, high-dimensional optimization, and applied stochastic processes. Springer previously published his books Mathematical and Statistical Methods for Genetic Analysis, 2nd ed., Applied Probability, and Optimization. He has written over 200 research papers and produced with his UCLA colleague Eric Sobel the computer program Mendel, widely used in statistical genetics.

- Series:
**Statistics and Computing** - Author:
**Kenneth Lange (auth.)** - Year:
**2010** - Publisher:
**Springer-Verlag New York** - Language:
**English** - ISBN:
**1441959440,978-1-4419-5944-7,978-1-4419-5945-4**

- File size:
**3 760 170** - Format:
**pdf**

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Written for graduate students in applied mathematics, engineering and science courses, the purpose of this book is to present topics in "Numerical Analysis" and "Numerical Methods." It will combine the material of both these areas as well as special topic...

It is not easy for engineers to gain all the skills necessary to perform numerical analysis. This book is an authoritative guide that explains in detail the potential restrictions and pitfalls and so help engineers undertake advanced numerical analysis. I...

This long-awaited Second Edition of Phillips and Taylor's highly successful text book provides a comprehensive introduction to numerical analysis. Over the two decades since the First Edition appeared there has been a dramatic explosion in computing power...

Researchers in many branches of science are increasingly coming into contact with Bayesian statistics or Bayesian probability theory. This book provides a clear exposition of the underlying concepts with large numbers of worked examples and problem sets. ...

Researchers in many branches of science are increasingly coming into contact with Bayesian statistics or Bayesian probability theory. This book provides a clear exposition of the underlying concepts with large numbers of worked examples and problem sets. ...

This book presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance among theoretical, algorithmic and...

This book covers numerical methods for partial differential equations: discretization methods such as finite difference, finite volume and finite element methods; solution methods for linear and nonlinear systems of equations and grid generation. The book...

The theory of elastoplastic media is now a mature branch of solid and structural mechanics, having experienced significant development during the latter half of this century. This monograph focuses on theoretical aspects of the small-strain theory of har...

Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward i...

'Author tackles a lack of self-esteem and the need to please others as a major problem in relationships and offers guidance via Christian belief and values'--Provided by the publisher. Facing fear and finding freedom -- Knowing who you are -- Conformi...

The history of word class research is characterized by two extreme positions. Up to the 19th century, it was believed that word classes were invariably of the Latin or Greek type and universal. In contrast to that, in the 20th century, the view prevailed ...

Compte tenu de l'int?r?t suscit? par la m?decine chinoise en Europe, cet ouvrage pr?sente pour la premi?re fois une analyse de l'histoire des id?es en m?decine chinoise depuis ses d?buts, il y a plus de deux mill?naires jusqu'`nos jours, associ?e `une com...

This book presents results on the convergence behavior of algorithms which are known as vital tools for solving convex feasibility problems and common fixed point problems. The main goal for us in dealing with a known computational error is to find what a...

Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requi...