Applied Probability / by Kenneth Lange
(Springer Texts in Statistics ; 0)
| データ種別 | 電子ブック |
|---|---|
| 版 | Second |
| 出版者 | New York, NY : Springer New York |
| 出版年 | 2010 |
| 本文言語 | 英語 |
| 大きさ | XVI, 436 p : online resource |
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| 内容注記 | Basic Notions of Probability Theory Calculation of Expectations Convexity, Optimization, and Inequalities Combinatorics Combinatorial Optimization Poisson Processes Discrete-Time Markov Chains Continuous-Time Markov Chains Branching Processes Martingales Diffusion Processes Asymptotic Methods Numerical Methods Poisson Approximation Number Theory Appendix: Mathematical Review |
|---|---|
| 一般注記 | Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. It can serve as a textbook for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. Readers should have a working knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes. If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. The second edition adds two new chapters on asymptotic and numerical methods and an appendix that separates some of the more delicate mathematical theory from the steady flow of examples in the main text. Besides the two new chapters, the second edition includes a more extensive list of exercises, many additions to the exposition of combinatorics, new material on rates of convergence to equilibrium in reversible Markov chains, a discussion of basic reproduction numbers in population modeling, and better coverage of Brownian motion. Because many chapters are nearly self-contained, mathematical scientists from a variety of backgrounds will find Applied Probability useful as a reference. Kenneth Lange is the Rosenfeld Professor of Computational Genetics in the Departments of Biomathematics and Human Genetics at the UCLA School of Medicine and the Chair of the Department of Human Genetics. 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., Numerical Analysis for Statisticians, 2nd ed., 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 |
| 著者標目 | *Lange, Kenneth author SpringerLink (Online service) |
| 件 名 | LCSH:Statistics LCSH:Mathematical statistics LCSH:Computer simulation LCSH:Computer mathematics LCSH:Probabilities LCSH:Biomathematics FREE:Statistics FREE:Statistical Theory and Methods FREE:Probability Theory and Stochastic Processes FREE:Probability and Statistics in Computer Science FREE:Mathematical and Computational Biology FREE:Computational Mathematics and Numerical Analysis FREE:Simulation and Modeling |
| 分 類 | DC23:519.5 |
| 巻冊次 | ISBN:9781441971654 
|
| ISBN | 9781441971654 |
| URL | http://dx.doi.org/10.1007/978-1-4419-7165-4 |
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