Principles of Statistical Genomics (eBook)

Shizhong Xu, PhD University of California, Department of Botany and Plant Sciences, Riverside, CA, USA

Part I Genetic Linkage Map
1 Map Functions
1.1 Physical map and genetic map
1.2 Derivation of map functions
1.3 Haldane map function
1.4 Kosambi map function
2 Recombination Fraction
2.1 Mating designs
2.2 Maximum likelihood estimation of recombination fraction
2.3 Standard error and significance test
2.4 Fisher’s scoring algorithm for estimating
2.5 EM algorithm for estimating
3 Genetic Map Construction
3.1 Criteria of optimality
3.2 Search algorithms
3.2.1 Exhaustive search
3.2.2 Heuristic search
3.2.3 Simulated annealing
3.2.4 Branch and bound
3.3 Bootstrap confidence of a map
4 Multipoint Analysis of Mendelian Loci
4.1 Joint distribution of multiple locus genotype
4.1.1 BC design
4.1.2 F2 design
4.1.3 Four-way cross design
4.2 Incomplete genotype information
4.2.1 Partially informative genotype
4.2.2 BC and F2 are special cases of FW
4.2.3 Dominance and missing markers
4.3 Conditional probability of a missing marker genotype
4.4 Joint estimation of recombination fractions
4.5 Multipoint analysis for m markers
4.6 Map construction with unknown recombination fractions
Part II Analysis of Quantitative Traits
5 Basic Concepts of Quantitative Genetics
5.1 Gene frequency and genotype frequency
5.2 Genetic effects and genetic variance
5.3 Average effect of allelic substitution
5.4 Genetic variance components
5.5 Heritability
5.6 An F2 family is in Hardy-Weinberg equilibrium
6 Major Gene Detection
6.1 Estimation of major gene effect
6.1.1 BC design
6.1.2 F2 design
6.2 Hypothesis tests
6.2.1 BC design
6.2.2 F2 design
6.3 Scale of the genotype indicator variable
6.4 Statistical power
6.4.1 Type I error and statistical power
6.4.2 Wald-test statistic
6.4.3 Size of a major gene
6.4.4 Relationship between W-test and Z-test
6.4.5 Extension to dominance effect
7 Segregation Analysis
7.1 Gaussian mixture distribution
7.2 EM algorithm
7.2.1 Closed form solution
7.2.2 EM steps
7.2.3 Derivation of the EM algorithm
7.2.4 Proof of the EM algorithm
7.3 Hypothesis tests
7.4 Variances of estimated parameters
7.5 Estimation of the mixing proportions
8 Genome Scanning for Quantitative Trait Loci
8.1 The mouse data
8.2 Genome scanning
8.3 Missing genotypes
8.4 Test statistics
8.5 Bonferroni correction
8.6 Permutation test
8.7 Piepho’s approximate critical value
8.8 Theoretical consideration
9 Interval Mapping
9.1 Least squares method
9.2 Weighted least squares
9.3 Fisher scoring
9.4 Maximum likelihood method
9.4.1 EM algorithm
9.4.2 Variance-covariance matrix of ˆθ
9.4.3 Hypothesis test
9.5 Remarks on the four methods of interval mapping
10 Interval Mapping for Ordinal Traits
10.1 Generalized linear model
10.2 ML under homogeneous variance
10.3 ML under heterogeneous variance
10.4 ML under mixture distribution
10.5 ML via the EM algorithm
10.6 Logistic analysis
10.7 Example
11 Mapping Segregation Distortion Loci
11.1 Probabilistic model
11.1.1 The EM Algorithm
11.1.2 Hypothesis test
11.1.3 Variance matrix of the estimated parameters
11.1.4 Selection coefficient and dominance
11.2 Liability model
11.2.1 EM algorithm
11.2.2 Variance matrix of estimated parameters
11.2.3 Hypothesis test
11.3 Mapping QTL under segregation distortion
11.3.1 Joint likelihood function
11.3.2 EM algorithm
11.3.3 Variance-covariance matrix of estimated parameters
11.3.4 Hypothesis tests
11.3.5 Example
12 QTL Mapping in Other Populations
12.1 Recombinant inbred lines
12.2 Double haploids
12.3 Four-way crosses
12.4 Full-sib family
12.5 F2 population derived from outbreds
12.6 Example
13 Random Model Approach to QTL Mapping
13.1 Identity-by-descent (IBD)
13.2 Random effect genetic model
13.3 Sib-pair regression
13.4 Maximum likelihood estimation
13.4.1 EM algorithm
13.4.2 EM algorithm under singular value decomposition
13.4.3 Multiple siblings
13.5 Estimating the IBD value for a marker
13.6 Multipoint method for estimating the IBD value
13.7 Genome scanning and hypothesis tests
13.8 Multiple QTL model
13.9 Complex pedigree analysis
14 Mapping QTL for Multiple Traits
14.1 Multivariate model
14.2 EM algorithm for parameter estimation
14.3 Hypothesis tests
14.4 Variance matrix of estimated parameters
14.5 Derivation of the EM algorithm
14.6 Example
15 Bayesian Multiple QTL Mapping
15.1 Bayesian regression analysis
15.2 Markov chain Monte Carlo
15.3 Mapping multiple QTL
15.3.1 Multiple QTL model
15.3.2 Prior, likelihood and posterior
15.3.3 Summary of the MCMC process
15.3.4 Post MCMC analysis
15.4 Alternative methods of Bayesian mapping
15.4.1 Reversible jump MCMC
15.4.2 Stochastic search variable selection
15.4.3 Lasso and Bayesian Lasso
15.5 Example: Arabidopsis data
16 Empirical Bayesian QTL Mapping
16.1 Classical mixed model
16.1.1 Simultaneous updating for matrix G
16.1.2 Coordinate descent method
16.1.3 Block coordinate descent method
16.1.4 Bayesian estimates of QTL effects
16.2 Hierarchical mixed model
16.2.1 Inverse chi-square prior
16.2.2 Exponential prior
16.2.3 Dealing with sparse models
16.3 Infinitesimal model for whole genome sequence data
16.3.1 Data trimming
16.3.2 Concept of continuous genome
16.4 Example: Simulated data
Part III Microarray Data Analysis
17 Microarray Differential Expression Analysis
17.1 Data preparation
17.1.1 Data transformation
17.1.2 Data normalization
17.2 F-test and t-test
17.3 Type I error and false discovery rate
17.4 Selection of differentially expressed genes
17.4.1 Permutation test
17.4.2 Selecting genes by controlling FDR
17.4.3 Problems of the previous methods
17.4.4 Regularized t-test
17.5 General linear model
17.5.1 Fixed model approach
17.5.2 Random model approach
18 Hierarchical Clustering of Microarray Data
18.1 Distance matrix
18.2 UPGMA
18.3 Neighbor joining
18.3.1 Principle of neighbor joining
18.3.2 Computational algorithm
18.4 Other methods
18.5 Bootstrap confidence
19 Model-Based Clustering of Microarray Data
19.1 Cluster analysis with the K-means method
19.2 Cluster analysis under Gaussian mixture
19.2.1 Multivariate Gaussian distribution
19.2.2 Mixture distribution
19.2.3 The EM algorithm
19.2.4 Supervised cluster analysis
19.2.5 Semi-supervised cluster analysis
19.3 Inferring the number of clusters
19.4 Microarray experiments with replications
20 Gene Specific Analysis of Variances
20.1 General linear model
20.2 The SEM algorithm
20.3 Hypothesis testing
21 Factor Analysis of Microarray Data
21.1 Background of factor analysis
21.1.1 Linear model of latent factors
21.1.2 EM algorithm
21.1.3 Number of factors
21.2 Cluster analysis
21.3 Differential expression analysis
21.4 MCMC algorithm
22 Classification of Tissue Samples Using Microarrays
22.1 Logistic regression
22.2 Penalized logistic regression
22.3 The coordinate descent algorithm
22.4 Cross validation
22.5 Prediction of disease outcome
22.6 Multiple category classification
23 Time-Course Microarray Data Analysis
23.1 Gene expression profiles
23.2 Orthogonal polynomial
23.3 B-spline
23.4 Mixed effect model
23.5 Mixture mixed model
23.6 EM algorithm
23.7 Best linear unbiased prediction
23.8 SEM algorithm
23.8.1 Monte Carlo sampling
23.8.2 SEM steps
24 Quantitative Trait Associated Microarray Data Analysis
24.1 Linear association
24.1.1 Linear model
24.1.2 Cluster analysis
24.1.3 Three-cluster analysis
24.1.4 Differential expression analysis
24.2 Polynomial and B-spline
24.3 Multiple trait association
25 Mapping Expression Quantitative Trait Loci
25.1 Individual marker analysis
25.1.1 SEM algorithm
25.1.2 MCMC algorithm
25.2 Joint analysis of all markers
25.2.1 Multiple eQTL model
25.2.2 SEM algorithm
25.2.3 MCMC algorithm
25.2.4 Hierarchical evolutionary stochastic search (HESS)