Applied Probability

  • Kenneth┬áLange

Part of the Springer Texts in Statistics book series (STS, volume 0)

Table of contents

  1. Front Matter
    Pages 1-14
  2. Kenneth Lange
    Pages 1-23
  3. Kenneth Lange
    Pages 25-53
  4. Kenneth Lange
    Pages 55-73
  5. Kenneth Lange
    Pages 75-101
  6. Kenneth Lange
    Pages 103-122
  7. Kenneth Lange
    Pages 123-150
  8. Kenneth Lange
    Pages 151-185
  9. Kenneth Lange
    Pages 187-215
  10. Kenneth Lange
    Pages 217-245
  11. Kenneth Lange
    Pages 247-268
  12. Kenneth Lange
    Pages 269-295
  13. Kenneth Lange
    Pages 297-325
  14. Kenneth Lange
    Pages 327-354
  15. Kenneth Lange
    Pages 355-372
  16. Kenneth Lange
    Pages 373-393
  17. Kenneth Lange
    Pages 395-413
  18. Back Matter
    Pages 418-418

About this book

Introduction

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.

Keywords

Branching process Markov chain Martingale Poisson process Probability theory Stochastic processes calculus combinatorics continuous-time Markov chain diffusion process linear algebra measure theory modeling number theory statistics

Authors and affiliations

  • Kenneth┬áLange
    • 1
  1. 1.UCLA School of Medicine, Depts. of Biomathematics, Human GeneticsUniversity of CaliforniaLos AngelesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-7165-4
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-7164-7
  • Online ISBN 978-1-4419-7165-4
  • Series Print ISSN 1431-875X
  • About this book