Applied Probability

1. Front Matter

   Pages i-xvii

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2. Basic Principles of Population Genetics

   Pages 1-20

3. Counting Methods and the EM Algorithm

   Pages 21-38

4. Newton’s Method and Scoring

   Pages 39-58

5. Hypothesis Testing and Categorical Data

   Pages 59-79

6. Genetic Identity Coefficients

   Pages 81-96

7. Applications of Identity Coefficients

   Pages 97-114

8. Computation of Mendelian Likelihoods

   Pages 115-139

9. The Polygenic Model

   Pages 141-168

10. Descent Graph Methods

    Pages 169-201

11. Molecular Phylogeny

    Pages 203-229

12. Radiation Hybrid Mapping

    Pages 231-255

13. Models of Recombination

    Pages 257-280

14. Sequence Analysis

    Pages 281-297

15. Poisson Approximation

    Pages 299-316

16. Diffusion Processes

    Pages 317-339

17. Back Matter

    Pages 341-367

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Despite the fears of university mathematics departments, mathematics educat,ion is growing rather than declining. But the truth of the matter is that the increases are occurring outside departments of mathematics. Engineers, computer scientists, physicists, chemists, economists, statis- cians, biologists, and even philosophers teach and learn a great deal of mathematics. The teaching is not always terribly rigorous, but it tends to be better motivated and better adapted to the needs of students. In my own experience teaching students of biostatistics and mathematical bi- ogy, I attempt to convey both the beauty and utility of probability. This is a tall order, partially because probability theory has its own vocabulary and habits of thought. The axiomatic presentation of advanced probability typically proceeds via measure theory. This approach has the advantage of rigor, but it inwitably misses most of the interesting applications, and many applied scientists rebel against the onslaught of technicalities. In the current book, I endeavor to achieve a balance between theory and app- cations in a rather short compass. While the combination of brevity apd balance sacrifices many of the proofs of a rigorous course, it is still cons- tent with supplying students with many of the relevant theoretical tools. In my opinion, it better to present the mathematical facts without proof rather than omit them altogether.

• Analysis
• Markov
• Measure
• Probability theory
• algorithm
• biostatistics
• combinatorial optimization
• combinatorics
• expectation–maximization algorithm
• linear algebra
• mathematical modeling
• model
• modeling
• numerical analysis
• optimization

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)

• Department of Biomathematics, UCLA School of Medicine, Los Angeles, USA

  Kenneth Lange

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