Applied Probability (Lange, Kenneth ) -- Springer Texts in Statistics

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Editorial ReviewsReview
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)

Product Description
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. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, and applied stochastic processes. Springer-Verlag published his books Numerical Analysis for Statisticians and Mathematical and Statistical Methods for Genetic Analysis Second Edition, in 1999 and 2002, respectively.

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关键词：Probability Statistics statistic Springer bability different providing include reviews written

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Product Details

• Hardcover: 320 pages
• Publisher: Springer (October 20, 2004)
• Language: English
• ISBN-10: 0387004254
• ISBN-13: 978-0387004259
• Product Dimensions: 9.5 x 6.4 x 0.8 inches
• Shipping Weight: 1.3 pounds (View shipping rates and policies)

Contents
Preface to the Second Edition vii
Preface to the First Edition ix
0.1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
1 Basic Principles of Population Genetics 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Genetics Background . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Hardy-Weinberg Equilibrium . . . . . . . . . . . . . . . . . 4
1.4 Linkage Equilibrium . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.6 Balance Between Mutation and Selection . . . . . . . . . . 12
1.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Counting Methods and the EM Algorithm 21
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Gene Counting . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Description of the EM Algorithm . . . . . . . . . . . . . . . 23
2.4 Ascent Property of the EM Algorithm . . . . . . . . . . . . 24
2.5 Allele Frequency Estimation by the EM Algorithm . . . . . 26
2.6 Classical Segregation Analysis by the EM Algorithm . . . . 27
2.7 Binding Domain Identification . . . . . . . . . . . . . . . . . 31
2.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3 Newton’s Method and Scoring 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Newton’s Method . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Scoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 Application to the Design of Linkage Experiments . . . . . 43
3.5 Quasi-Newton Methods . . . . . . . . . . . . . . . . . . . . 45
3.6 The Dirichlet Distribution . . . . . . . . . . . . . . . . . . . 47
3.7 Empirical Bayes Estimation of Allele Frequencies . . . . . . 48
3.8 Empirical Bayes Estimation of Haplotype Frequencies . . . 51
3.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 Hypothesis Testing and Categorical Data 59
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Hypotheses About Genotype Frequencies . . . . . . . . . . 59
4.3 Other Multinomial Problems in Genetics . . . . . . . . . . . 62
4.4 The Zmax Test . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.5 The Wd Statistic . . . . . . . . . . . . . . . . . . . . . . . . 65
4.6 Exact Tests of Independence . . . . . . . . . . . . . . . . . 67
4.7 Case-Control Association Tests . . . . . . . . . . . . . . . . 69
4.8 The Transmission/Disequilibrium Test . . . . . . . . . . . . 70
4.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5 Genetic Identity Coefficients 81
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2 Kinship and Inbreeding Coefficients . . . . . . . . . . . . . . 81
5.3 Condensed Identity Coefficients . . . . . . . . . . . . . . . . 84
5.4 Generalized Kinship Coefficients . . . . . . . . . . . . . . . 86
5.5 From Kinship to Identity Coefficients . . . . . . . . . . . . . 86
5.6 Calculation of Generalized Kinship Coefficients . . . . . . . 88
5.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6 Applications of Identity Coefficients 97
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2 Genotype Prediction . . . . . . . . . . . . . . . . . . . . . . 97
6.3 Covariances for a Quantitative Trait . . . . . . . . . . . . . 99
6.4 Risk Ratios and Genetic Model Discrimination . . . . . . . 102
6.5 An Affecteds-Only Method of Linkage Analysis . . . . . . . 106
6.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

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7 Computation of Mendelian Likelihoods 115
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.2 Mendelian Models . . . . . . . . . . . . . . . . . . . . . . . 115
7.3 Genotype Elimination and Allele Consolidation . . . . . . . 118
7.4 Array Transformations and Iterated Sums . . . . . . . . . . 120
7.5 Array Factoring . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.6 Examples of Pedigree Analysis . . . . . . . . . . . . . . . . 124
7.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8 The Polygenic Model 141
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.2 Maximum Likelihood Estimation by Scoring . . . . . . . . . 142
8.3 Application to Gc Measured Genotype Data . . . . . . . . . 146
8.4 Multivariate Traits . . . . . . . . . . . . . . . . . . . . . . . 147
8.5 Left and Right-Hand Finger Ridge Counts . . . . . . . . . . 149
8.6 QTL Mapping . . . . . . . . . . . . . . . . . . . . . . . . . 150
8.7 Factor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 151
8.8 A QTL Example . . . . . . . . . . . . . . . . . . . . . . . . 152
8.9 The Hypergeometric Polygenic Model . . . . . . . . . . . . 154
8.10 Application to Risk Prediction . . . . . . . . . . . . . . . . 157
8.11 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
8.12 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
9 Descent Graph Methods 169
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
9.2 Review of Discrete-Time Markov Chains . . . . . . . . . . . 170
9.3 The Hastings-Metropolis Algorithm and Simulated Annealing173
9.4 Descent States and Descent Graphs . . . . . . . . . . . . . . 175
9.5 Descent Trees and the Founder Tree Graph . . . . . . . . . 177
9.6 The Descent Graph Markov Chain . . . . . . . . . . . . . . 181
9.7 Computing Location Scores . . . . . . . . . . . . . . . . . . 184
9.8 Finding a Legal Descent Graph . . . . . . . . . . . . . . . . 185
9.9 Haplotyping . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
9.10 Application to Episodic Ataxia . . . . . . . . . . . . . . . . 187
9.11 The Lander-Green-Kruglyak Algorithm . . . . . . . . . . . 188
9.12 Genotyping Errors . . . . . . . . . . . . . . . . . . . . . . . 191
9.13 Marker Sharing Statistics . . . . . . . . . . . . . . . . . . . 192
9.14 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
9.15 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
10 Molecular Phylogeny 203
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
10.2 Evolutionary Trees . . . . . . . . . . . . . . . . . . . . . . . 203
10.3 Maximum Parsimony . . . . . . . . . . . . . . . . . . . . . . 205
10.4 Review of Continuous-Time Markov Chains . . . . . . . . . 209
10.5 A Nucleotide Substitution Model . . . . . . . . . . . . . . . 211
10.6 Maximum Likelihood Reconstruction . . . . . . . . . . . . . 214
10.7 Origin of the Eukaryotes . . . . . . . . . . . . . . . . . . . . 215
10.8 CodonModels . . . . . . . . . . . . . . . . . . . . . . . . . 218
10.9 Variation in the Rate of Evolution . . . . . . . . . . . . . . 219
10.10Illustration of the Codon and Rate Models . . . . . . . . . . 221
10.11Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
10.12References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
11 Radiation Hybrid Mapping 231
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
11.2 Models for Radiation Hybrids . . . . . . . . . . . . . . . . . 232
11.3 Minimum Obligate Breaks Criterion . . . . . . . . . . . . . 233
11.4 Maximum Likelihood Methods . . . . . . . . . . . . . . . . 236
11.5 Application to Haploid Data . . . . . . . . . . . . . . . . . 238
11.6 Polyploid Radiation Hybrids . . . . . . . . . . . . . . . . . 239
11.7 Maximum Likelihood Under Polyploidy . . . . . . . . . . . 240
11.8 Obligate Breaks Under Polyploidy . . . . . . . . . . . . . . 244
11.9 Bayesian Methods . . . . . . . . . . . . . . . . . . . . . . . 245
11.10Application to Diploid Data . . . . . . . . . . . . . . . . . . 248
11.11Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
11.12References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
12 Models of Recombination 257
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
12.2 Mather’s Formula and Its Generalization . . . . . . . . . . . 258
12.3 Count-Location Model . . . . . . . . . . . . . . . . . . . . . 260
12.4 Stationary Renewal Models . . . . . . . . . . . . . . . . . . 261
12.5 Poisson-Skip Model . . . . . . . . . . . . . . . . . . . . . . . 264
12.6 Chiasma Interference . . . . . . . . . . . . . . . . . . . . . . 270
12.7 Application to Drosophila Data . . . . . . . . . . . . . . . . 273
12.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
12.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
13 Sequence Analysis 281
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
13.2 Pattern Matching . . . . . . . . . . . . . . . . . . . . . . . . 281
13.3 Alphabets, Strings, and Alignments . . . . . . . . . . . . . . 283
13.4 Minimum Distance Alignment . . . . . . . . . . . . . . . . . 285
13.5 Parallel Processing and Memory Reduction . . . . . . . . . 289
13.6 Maximum Similarity Alignment . . . . . . . . . . . . . . . . 290
13.7 Local Similarity Alignment . . . . . . . . . . . . . . . . . . 291
13.8 Multiple Sequence Comparisons . . . . . . . . . . . . . . . . 292
13.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
14 Poisson Approximation 299
14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
14.2 The Law of Rare Events . . . . . . . . . . . . . . . . . . . . 300
14.3 Poisson Approximation to the Wd Statistic . . . . . . . . . 300
14.4 Construction of Somatic Cell Hybrid Panels . . . . . . . . . 301
14.5 Biggest Marker Gap . . . . . . . . . . . . . . . . . . . . . . 304
14.6 Randomness of Restriction Sites . . . . . . . . . . . . . . . 306
14.7 DNA Sequence Matching . . . . . . . . . . . . . . . . . . . 308
14.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
14.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
15 Diffusion Processes 317
15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
15.2 Review of Diffusion Processes . . . . . . . . . . . . . . . . . 317
15.3 Wright-Fisher Model . . . . . . . . . . . . . . . . . . . . . . 321
15.4 First Passage Time Problems . . . . . . . . . . . . . . . . . 322
15.5 Process Moments . . . . . . . . . . . . . . . . . . . . . . . . 325
15.6 Equilibrium Distribution . . . . . . . . . . . . . . . . . . . . 326
15.7 Numerical Methods for Diffusion Processes . . . . . . . . . 328
15.8 Numerical Methods for the Wright-Fisher Process . . . . . 332
15.9 Specific Example for a Recessive Disease . . . . . . . . . . . 333
15.10Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
15.11References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
Appendix A: Molecular Genetics in Brief 341
A.1 Genes and Chromosomes . . . . . . . . . . . . . . . . . . . . 341
A.2 From Gene to Protein . . . . . . . . . . . . . . . . . . . . . 343
A.3 Manipulating DNA . . . . . . . . . . . . . . . . . . . . . . . 345
A.4 Mapping Strategies . . . . . . . . . . . . . . . . . . . . . . . 346
A.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
Appendix B: The Normal Distribution 351
B.1 Univariate Normal Random Variables . . . . . . . . . . . . 351
B.2 Multivariate Normal Random Vectors . . . . . . . . . . . . 352
B.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
Index 355

帮你补充一点出版信息,否则也没有人知道里面讲些什么东西 Applied Probability 丛书 Springer Texts in Statistics ISSN 1431-875X 学科 Mathematics, Probability Theory and Stochastic Processes and Statistical Theory and Methods 出版社 Springer New York DOI 10.1007/b98849 版权 2003 ISBN 978-0-387-00425-9 (Print) 978-0-387-22711-5 (Online) 学科分类 数学和统计学 学科 Mathematics, Probability Theory and Stochastic Processes and Statistical Theory and Methods SpringerLink Date 2008年1月17日

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关闭突出显示        编辑信息   简要列表   详细列表             共 15 章          Front Matter PDF (740.6 KB)  i-xvii                   章节 Basic Principles of Population Genetics            PDF (241.2 KB)  1-20          章节 Counting Methods and the EM Algorithm            PDF (223.0 KB)  21-38          章节 Newton’s Method and Scoring            PDF (232.1 KB)  39-58          章节 Hypothesis Testing and Categorical Data            PDF (245.9 KB)  59-79          章节 Genetic Identity Coefficients            PDF (204.8 KB)  81-96          章节 Applications of Identity Coefficients            PDF (223.2 KB)  97-114          章节 Computation of Mendelian Likelihoods            PDF (251.2 KB)  115-139          章节 The Polygenic Model            PDF (283.0 KB)  141-168          章节 Descent Graph Methods            PDF (300.5 KB)  169-201          章节 Molecular Phylogeny            PDF (257.7 KB)  203-229          章节 Radiation Hybrid Mapping            PDF (255.4 KB)  231-255          章节 Models of Recombination            PDF (257.6 KB)  257-280          章节 Sequence Analysis            PDF (221.3 KB)  281-297          章节 Poisson Approximation            PDF (232.2 KB)  299-316          章节 Diffusion Processes            PDF (345.9 KB)  317-339          Back Matter PDF (532.0 KB)  341-367          共 15 章

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