About the Book
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.
Table of Contents:
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 * Poisson Approximation * Number Theory
Review :
From the reviews: "This book was written to convey both the 'beauty and utility of probability.' The author achieves this by providing a mixture of theory and application. To include so many different and interesting applications of probability, the author chose to minimize the number of proofs. Instead, he provides examples and written explanations!The unique aspect of this text is that the author presents applications not normally included in probability texts. There are new and very useful applications of probability that would usually be found in journal articles or in a number of different textbooks." Technometrics, May 2004 "!Pretty applications in computer science and genetics strengthen the overall message of this book, namely to give applied probability the attention it deserves." Short Book Reviews of the International Statistical Institute, April 2004 "In his Preface, he worries that the pursuit of mathematical rigor discourages students of science, particularly of biology, from learning the powerful tools that modern probability theory puts at their disposal. This book is an attempt to remedy that!Professor Lange's book is certainly a pleasure to read, and it is written in a clear style using standard probabilistic notation." Journal of the American Statistical Association, June 2004 "This book is intended for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics and statistics. ! The book presents a mixture of theory and applications, with emphasis on mathematical modeling and computational techniques. It contains a number of examples from the biological sciences. ! All chapters have exercises and hints are provided for some of the difficult problems. ! Students should find this book stimulating, refreshing and highly useful." (R. Subramanian, Mathematical Reviews, 2004a) "The book would be a delight to use. ! Lange has produced an enjoyable, highly readable book ! . I found much of the material of interest ! . All of the chapters come with exercises some of them challenging. ! a course based on this material would be a joy." (Jeffrey J. Hunter, New Zealand Mathematical Society Newsletter, Issue 89, December, 2003) "Lange makes every possible effort to keep a delicate balance between theory and applications. He presents the material in a clear and informative manner that will appeal to all interested readers ! . Lange offers numerous illustrative examples from biological sciences and challenging chapter end problems. This interesting and useful book presents clearly the applicability of probabilistic tools to solve problems in different disciplines. Summing Up: Recommended. Researchers and graduate students in genetics, mathematics, physics, biostatistics, computer science, and statistics." (D.V. Chopra, CHOICE, September, 2003) "The author tries to offer to the scientific community at large an introduction to some of the most important aspects of applied probability. From the table of contents, it is clear that the author has chosen a very personal approach ! . this choice illustrates the beauty, utility and relevance of probabilistic thinking in a variety of scientific areas. In particular, pretty applications in computer science and genetics strengthen the overall message of this book, namely to give applied probability the attention it deserves." (J.L. Teugels, Short Book Reviews, Vol. 24 (1), 2004)
