Principles of Statistical Genomics

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

Genetic Linkage Map.- Map Functions.- Physical map and genetic map.- Derivation of map functions.- Haldane map function.- Kosambi map function.- Recombination Fraction.- Mating designs.- Maximum likelihood estimation of recombination fraction.- Standard error and significance test.- Fisher’s scoring algorithm for estimating.- EM algorithm for estimating.- Genetic Map Construction.- Criteria of optimality.- Search algorithms.- Exhaustive search.- Heuristic search.- Simulated annealing.- Branch and bound.- Bootstrap confidence of a map.- Multipoint Analysis of Mendelian Loci.- Joint distribution of multiple locus genotype.- BC design.- F2 design.- Four-way cross design.- Incomplete genotype information.- Partially informative genotype.- BC and F2 are special cases of FW.- Dominance and missing markers.- Conditional probability of a missing marker genotype.- Joint estimation of recombination fractions.- Multipoint analysis for m markers.- Map construction with unknown recombination fractions.- Basic Concepts of Quantitative Genetics.- Gene frequency and genotype frequency.- Genetic effects and genetic variance.- Average effect of allelic substitution.- Genetic variance components.- Heritability.- An F2 family is in Hardy-Weinberg equilibrium.- Major Gene Detection.- Estimation of major gene effect.- BC design.- F2 design.- Hypothesis tests.- BC design.- F2 design.- Scale of the genotype indicator variable.- Statistical power.- Type I error and statistical power.- Wald-test statistic.- Size of a major gene.- Relationship between W-test and Z-test.- Extension to dominance effect.- Segregation Analysis.- Gaussian mixture distribution.- EM algorithm.- Closed form solution.- EM steps.- Derivation of the EM algorithm.- Proof of the EM algorithm.- Hypothesis tests.- Variances of estimated parameters.- Estimation of the mixing proportions.- Genome Scanning for Quantitative Trait Loci .- The mouse data.- Genome scanning.- Missing genotypes.- Test statistics.- Bonferroni correction.- Permutation test.- Piepho’s approximate critical value.- Theoretical consideration.- Interval Mapping.- Least squares method.- Weighted least squares.- Fisher scoring.- Maximum likelihood method.- EM algorithm.- Variance-covariance matrix of ˆθ.- Hypothesis test.- Remarks on the four methods of interval mapping.- Interval Mapping for Ordinal Traits.- Generalized linear model.- ML under homogeneous variance.- ML under heterogeneous variance.- ML under mixture distribution.- ML via the EM algorithm.- Logistic analysis.- Example.- Mapping Segregation Distortion Loci.- Probabilistic model.- The EM Algorithm.- Hypothesis test.- Variance matrix of the estimated parameters.- Selection coefficient and dominance.- Liability model.- EM algorithm.- Variance matrix of estimated parameters.- Hypothesis test.- Mapping QTL under segregation distortion.- Joint likelihood function.- EM algorithm.- Variance-covariance matrix of estimated parameters.- Hypothesis tests.- Example.- QTL Mapping inOther Populations.- Recombinant inbred lines.- Double haploids.- Four-way crosses.- Full-sib family.- F2 population derived from outbreds.- Example.- Random Model Approach to QTL Mapping.- Identity-by-descent (IBD).- Random effect genetic model.- Sib-pair regression.-  Maximum likelihood estimation.- EM algorithm.- EM algorithm under singular value decomposition.- Multiple siblings.- Estimating the IBD value for a marker.- Multipoint method for estimating the IBD value.- Genome scanning and hypothesis tests.- Multiple QTL model.- Complex pedigree analysis.- Mapping QTL for Multiple Traits.- Multivariate model.- EM algorithm for parameter estimation.- Hypothesis tests.- Variance matrix of estimated parameters.- Derivation of the EM algorithm.- Example.- Bayesian Multiple QTL Mapping.- Bayesian regression analysis.- Markov chain Monte Carlo.- Mapping multiple QTL.- Multiple QTL model.- Prior, likelihood and posterior.- Summary of the MCMC process.- Post MCMC analysis.- Alternative methods of Bayesian mapping.- Reversible jump MCMC.- Stochastic search variable selection.- Lasso and Bayesian Lasso.- Example: Arabidopsis data.- Empirical Bayesian QTL Mapping.- Classical mixed model.- Simultaneous updating for matrix G.- Coordinate descent method.- Block coordinate descent method.- Bayesian estimates of QTL effects.- Hierarchical mixed model.- Inverse chi-square prior.- Exponential prior.- Dealing with sparse models.- Infinitesimal model for whole genome sequence data.- Data trimming.- Concept of continuous genome.- Example: Simulated data.- Microarray Differential Expression Analysis.- Data preparation.- Data transformation.- Data normalization.- F-test and t-test.- Type I error and false discovery rate.- Selection of differentially expressed genes.- Permutation test.- Selecting genes by controlling FDR.- Problems of the previous methods.- Regularized t-test.- General linear model.- Fixed model approach.- Random model approach.- Hierarchical Clustering of Microarray Data.- Distance matrix.- UPGMA.- Neighbor joining.- Principle of neighbor joining.- Computational algorithm.- Other methods.- Bootstrap confidence.- Model-Based Clustering of Microarray Data.- Cluster analysis with the K-means method.- Cluster analysis under Gaussian mixture.- Multivariate Gaussian distribution.- Mixture distribution.- The EM algorithm.- Supervised cluster analysis.- Semi-supervised cluster analysis.- Inferring the number of clusters.- Microarray experiments with replications.- Gene Specific Analysis of Variances.- General linear model.- The SEM algorithm.- Hypothesis testing.- Factor Analysis of Microarray Data.- Background of factor analysis.- Linear model of latent factors.- EM algorithm.- Number of factors.- Cluster analysis.- Differential expression analysis.- MCMC algorithm.- Classification of Tissue Samples Using Microarrays.- Logistic regression.- Penalized logistic regression.- The coordinate descent algorithm.- Cross validation.- Prediction of disease outcome.- Multiple category classification.- Time-Course Microarray Data Analysis.- Gene expression profiles.- Orthogonal polynomial.- B-spline.- Mixed effect model.- Mixture mixed model.- EM algorithm.- Best linear unbiased prediction.- SEM algorithm.- Monte Carlo sampling.- SEM steps.- Quantitative Trait Associated Microarray Data Analysis.- Linear association.- Linear model.- Cluster analysis.- Three-cluster analysis.- Differential expres.- SEM algorithm.- MCMC algorithm.- Joint analysis of all markers.- Multiple eQTL model.- SEM algorithm.- MCMC algorithm.- Hierarchical evolutionary stochastic search (HESS).