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Numerical Analysis for Stat...
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
Monografía
monografia Rebiun11867261 https://catalogo.rebiun.org/rebiun/record/Rebiun11867261 cr nn 008mamaa 100528s2010 xxu| s |||| 0|eng d 9781441959454 10.1007/978-1-4419-5945-4 doi UPVA 996877342203706 UAM 991007632929604211 CUNEF 991000429741108131 CBUC 991004877209406711 CBUC 991010402156106709 UR0317405 UFM bicssc COM077000 bisacsh 519.5 23 Lange, Kenneth Numerical Analysis for Statisticians Recurso electrónico-En línea] by Kenneth Lange New York, NY Springer New York 2010 New York, NY New York, NY Springer New York XVI, 604p. digital XVI, 604p. Statistics and Computing 1431-8784 Mathematics and Statistics (Springer-11649) 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 Accesible sólo para usuarios de la UPV Recurso a texto completo 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 Reproducción electrónica Forma de acceso: Web Statistics Mathematical statistics Statistics Statistics and Computing/Statistics Programs SpringerLink (Servicio en línea) Springer eBooks Springer eBooks Printed edition 9781441959447 Statistics and Computing 1431-8784