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During the past decade, geneticists have constructed detailed maps of the human genome and cloned scores of Mendelian disease genes. They now stand on the threshold of sequencing the genome in its entirety. The unprecedented insights into human disease and evolution offered by mapping and sequencing will transform medicine and agriculture. This revolution depends vitally on the contributions of applied mathematicians, statisticians, and computer scientists. Mathematical and Statistical Methods for Genetic Analysis is written to equip graduate students in the mathematical sciences to understand and model the epidemiological and experimental data encountered in genetics research. Mathematical, statistical, and computational principles relevant to this task are developed hand in hand with applications to gene mapping, risk prediction, and the testing of epidemiological hypotheses. The book includes many topics currently accessible only in journal articles, including pedigree analysis algorithms, Markov chain Monte Carlo methods, reconstruction of evolutionary trees, radiation hybrid mapping, and models of recombination. Exercise sets are included. Kenneth Lange is Professor of Biostatistics and Mathematics and the Pharmacia & Upjohn Foundations Research Professor at the University of Michigan. He has held visiting appointments at MIT and Harvard. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, and applied stochastic processes.
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 Markov Chain Monte Carlo Methods.- 10 Reconstruction of Evolutionary Trees.- 11 Radiation Hybrid Mapping.- 12 Models of Recombination.- 13 Poisson Approximation.- Appendix: Molecular Genetics in Brief.- A.l Genes and Chromosomes.- A.2 From Gene to Protein.- A.3 Manipulating DNA.- A.4 Mapping Strategies.- References.