Statistics in Human Genetics and Molecular Biology

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ISBN: 9781420072631 | 1420072633
Cover: Hardcover
Copyright: 6/19/2009

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Focusing on problems in contemporary genetics and molecular biology, this text describes basic statistical methods used in genetics. It covers cluster analysis, combinatorial optimization, and dynamic programming, along with the core topics of genome mapping, biological sequence analysis, and the analysis of gene expression arrays. The author also explores Bayesian approaches, such as hidden Markov models and block motif methods, as well as modern tools of Bayesian analysis, including Markov chain Monte Carlo (MCMC). The text features a number of worked examples and problem sets at the end of each chapter.

Preface	p. xi
Basic Molecular Biology for Statistical Genetics and Genomics	p. 1
Mendelian genetics	p. 1
Cell biology	p. 2
Genes and chromosomes	p. 3
DNA	p. 5
RNA	p. 6
Proteins	p. 7
Protein pathways and interactions	p. 9
Some basic laboratory techniques	p. 11
Bibliographic notes and further reading	p. 13
Exercises	p. 13
Basics of Likelihood Based Statistics	p. 15
Conditional probability and Bayes theorem	p. 15
Likelihood based inference	p. 16
The Poisson process as a model for chromosomal breaks	p. 17
Markov chains	p. 18
Poisson process continued	p. 19
Maximum likelihood estimates	p. 21
The EM algorithm	p. 26
Likelihood ratio tests	p. 28
Maximized likelihood ratio tests	p. 28
Empirical Bayes analysis	p. 29
Markov chain Monte Carlo sampling	p. 30
Bibliographic notes and further reading	p. 33
Exercises	p. 33
Markers and Physical Mapping	p. 37
Introduction	p. 37
Types of markers	p. 39
Restriction fragment length polymorphisms (RFLPs)	p. 40
Simple sequence length polymorphisms (SSLPs)	p. 40
Single nucleotide polymorphisms (SNPs)	p. 40
Physical mapping of genomes	p. 41
Restriction mapping	p. 41
Fluorescent in situ hybridization (FISH) mapping	p. 45
Sequence tagged site (STS) mapping	p. 46
Radiation hybrid mapping	p. 46
Experimental technique	p. 46
Data from a radiation hybrid panel	p. 46
Minimum number of obligate breaks	p. 47
Consistency of the order	p. 47
Maximum likelihood and Bayesian methods	p. 48
Exercises	p. 50
Basic Linkage Analysis	p. 53
Production of gametes and data for genetic mapping	p. 53
Some ideas from population genetics	p. 54
The idea of linkage analysis	p. 55
Quality of genetic markers	p. 61
Heterozygosity	p. 61
Polymorphism information content	p. 62
Two point parametric linkage analysis	p. 62
LOD scores	p. 63
A Bayesian approach to linkage analysis	p. 63
Multipoint parametric linkage analysis	p. 64
Quantifying linkage	p. 65
An example of multipoint computations	p. 66
Computation of pedigree likelihoods	p. 67
The Elston Stewart algorithm	p. 68
The Lander Green algorithm	p. 68
MCMC based approaches	p. 69
Sparse binary tree based approaches	p. 70
Exercises	p. 70
Extensions of the Basic Model for Parametric Linkage	p. 73
Introduction	p. 73
Penetrance	p. 74
Phenocopies	p. 75
Heterogeneity in the recombination fraction	p. 75
Heterogeneity tests	p. 76
Relating genetic maps to Physical maps	p. 77
Multilocus models	p. 80
Exercises	p. 81
Nonparametric Linkage and Association Analysis	p. 83
Introduction	p. 83
Sib-pair method	p. 83
Identity by descent	p. 84
Affected sib-pair (ASP) methods	p. 84
Tests for linkage with ASPs	p. 85
QTL mapping in human populations	p. 86
Haseman Elston regression	p. 87
Variance components models	p. 88
Coancestry	p. 89
Estimating IBD sharing in a chromosomal region	p. 90
A case study: dealing with heterogeneity in QTL mapping	p. 92
Linkage disequilibrium	p. 98
Association analysis	p. 100
Use of family based controls	p. 100
Haplotype relative risk	p. 101
Haplotype-based haplotype relative risk	p. 102
The transmission disequilibrium test	p. 103
Correcting for stratification using unrelated individuals	p. 104
The HAPMAP project	p. 106
Exercises	p. 106
Sequence Alignment	p. 109
Sequence alignment	p. 109
Dot plots	p. 110
Finding the most likely alignment	p. 111
Dynamic programming	p. 114
Using dynamic programming to find the alignment	p. 115
Some variations	p. 119
Global versus local alignments	p. 119
Exercises	p. 120
Significance of Alignments and Alignment in Practice	p. 123
Statistical significance of sequence similarity	p. 123
Distributions of maxima of sets of iid random variables	p. 124
Application to sequence alignment	p. 127
Rapid methods of sequence alignment	p. 128
FASTA	p. 130
BLAST	p. 130
Internet resources for computational biology	p. 132
Exercises	p. 133
Hidden Markov Models	p. 135
Statistical inference for discrete parameter finite state space Markov chains	p. 135
Hidden Markov models	p. 136
A simple binomial example	p. 136
Estimation for hidden Markov models	p. 137
The forward recursion	p. 137
The forward recursion for the binomial example	p. 138
The backward recursion	p. 138
The backward recursion for the binomial example	p. 139
The posterior mode of the state sequence	p. 140
Parameter estimation	p. 141
Parameter estimation for the binomial example	p. 142
Integration over the model parameters	p. 143
Simulating from the posterior of &ostroke;	p. 145
Using the Gibbs sampler to obtain simulations from the joint posterior	p. 145
Exercises	p. 146
Feature Recognition in Biopolymers	p. 147
Gene transcription	p. 149
Detection of transcription factor binding sites	p. 150
Consensus sequence methods	p. 150
Position specific scoring matrices	p. 151
Hidden Markov models for feature recognition	p. 153
A hidden Markov model for intervals of the genome	p. 153
A HMM for base-pair searches	p. 154
Computational gene recognition	p. 154
Use of weight matrices	p. 156
Classification based approaches	p. 156
Hidden Markov model based approaches	p. 157
Feature recognition via database sequence comparison	p. 159
The use of orthologous sequences	p. 159
Exercises	p. 160
Multiple Alignment and Sequence Feature Discovery	p. 161
Introduction	p. 161
Dynamic programming	p. 162
Progressive alignment methods	p. 163
Hidden Markov models	p. 165
Extensions	p. 167
Block motif methods	p. 168
Extensions	p. 172
The propagation model	p. 173
Enumeration based methods	p. 174
A case study: detection of conserved elements in mRNA	p. 175
Exercises	p. 177
Statistical Genomics	p. 179
Functional genomics	p. 179
The technology	p. 180
Spotted cDNA arrays	p. 181
Oligonucleotide arrays	p. 181
The MAS 5.0 algorithm for signal value computation	p. 182
Model based expression index	p. 184
Robust multi-array average	p. 185
Normalization	p. 187
Global (or linear) normalization	p. 188
Spatially varying normalization	p. 189
Loess normalization	p. 189
Quantile normalization	p. 190
Invariant set normalization	p. 190
Exercises	p. 190
Detecting Differential Expression	p. 193
Introduction	p. 193
Multiple testing and the false discovery rate	p. 194
Significance analysis for microarrays	p. 199
Gene level summaries	p. 199
Nonparametric inference	p. 200
The role of the data reduction	p. 202
Local false discovery rate	p. 203
Model based empirical Bayes approach	p. 203
A case study: normalization and differential detection	p. 207
Exercises	p. 211
Cluster Analysis in Genomics	p. 213
Introduction	p. 213
Dissimilarity measures	p. 215
Data standardization	p. 215
Filtering genes	p. 215
Some approaches to cluster analysis	p. 216
Hierarchical cluster analysis	p. 216
K-means cluster analysis and variants	p. 219
Model based clustering	p. 220
Determining the number of clusters	p. 223
Biclustering	p. 226
Exercises	p. 228
Classification in Genomics	p. 231
Introduction	p. 231
Cross-validation	p. 233
Methods for classification	p. 234
Discriminate analysis	p. 234
Regression based approaches	p. 237
Regression trees	p. 238
Weighted voting	p. 239
Nearest neighbor classifiers	p. 240
Support vector machines	p. 240
Aggregating classifiers	p. 244
Bagging	p. 244
Boosting	p. 245
Random forests	p. 246
Evaluating performance of a classifier	p. 246
Exercises	p. 247
References	p. 249
Index	p. 261
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