附註:Includes bibliographical references (pages 285-294) and index.
Cover -- Preface -- Table of Contents -- Preface to the Second Edition -- Preface to the First Edition -- 1. Basic Principles of Population Genetics -- 2. Counting Methods and the EM Algorithm -- 3. Newton's Method and Scoring -- 4. Hypothesis Testing and Categorical Data -- 5. Genetic Identity Coefficients -- 6. Applications of Identity Coefficients -- 7. Computation of Mendelian Likelihoods -- 8. The Polygenic Model -- 9. Descent Graph Methods -- 10. Molecular Phylogeny -- 11. Radiation Hybrid Mapping -- 12. Models of Recombination -- 13. Sequence Analysis -- 14. Poisson Approximation -- 15. Diffusion Processes -- Appendix A: Molecular Genetics in Brief -- Appendix B: The Normal Distribution.
摘要:This textbook on applied probability is intended for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. It presupposes knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Given these prerequisites, Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. 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 here for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. Finally, Chapters 12 and 13 develop the Chen-Stein method of Poisson approximation and connections between probability and number theory. Kenneth Lange is Professor of Biomathematics and Human Genetics and Chair of the Department of Human Genetics at the UCLA School of Medicine. He has held appointments at the University of New Hampshire, MIT, Harvard, and the University of Michigan. While at the University of Michigan, he was the Pharmacia & Upjohn Foundation Professor of Biostatistics.
