Page 13 - Applied Probability

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