Statistical Models in Genetics

Stat 367

Statistical Models in Genetics

This course will be cotaught by Ken Lange, a visiting professor from UCLA, and Chiara Sabatti. The course will feature statistical problems in genetics, with an emphasis on association and linkage analysis of qualitative and quantitative traits in human and experimental populations. The class will provide a broad outline of how statistical models help addressing the fundamental questions in genetic research. We will pay special attention to current research topics, illustrating the challenges presented by genomic data obtained via high-throughput technologies.

Students will be expected to have a good background in probability, statistics, mathematical analysis, and linear algebra. Familiarity with a programming language such as C, Fortran, Matlab, R, or Julia is required. Grades will be based on homework. Some lecture material will be drawn from the book Statistical and Mathematical Methods for Genetic Analysis by Professor Lange. Relevant chapters and other reading material will be made available by the instructors.

Depending on time and interest we will cover a selection of the following topics. As we move through the quarter entries will become more precise, reflecting the material actually presented in class, and including references.

Introduction to Genetics, models and data
- Mendel (1865) Experiments in Plant Hybridization (a revision of the Bateson's translation, 1901).
- Fisher (1936) Has Mendel's work been rediscovered? The Annals of Science.
- Korner (1988) Fourier Analysis, chapters 82-85.
- 1000 genomes project
- Encode project
- HapMap project
Principles of Population Genetics.
- Lecture notes available on Coursework.
Applied population genetics and Measures of Genetic Relationship
- Rosenberg et al (2002) Genetic structure of human populations, Science
- Alexander et al. (2009) Fast model-based estimation of ancestry in unrelated individuals, Genome Research
- Lecture notes available on Coursework.
Classical Polygenic Model
- Chapters 6 and 8 from Lange's book available on Coursework
- Hallmayer et al. (2011) Genetic heritability and shared environmental factors among twin pairs with autism Arch. General Psychiatry
- Gaugler et al. (2014) Most genetic risk for autism resides with common variation Nature Genetics
- Yang et al. (2010) Common SNPs explain a large proportion of the heritability for human height Nature Genetics
MM Principle in Parameter Estimation
- Lecture notes available on Coursework.
SVD and applications to Genotype Imputation
- Lecture notes available on Coursework.
Recombination models and linkage analysis
- Lecture notes on Coursework
- Haldane (1919) The combination of linkage values, and the calculation of distances between the loci of linked factors.
- Zhao and Speed (1996) On genetic map functions
- Feingold et al. (1993) Gaussian models for genetic linkage analysis using complete high-resolution maps of identity by descent.
- Sobel and Lange (1996) Descent graphs in pedigree analysis: applications to haplotyping, location scores, and marker-sharing statistics.
- E.A. Thompson (1996) Likelihood and linkage: from Fisher to the future
Association Testing
- Chapter 12 from Siegmund & Yakir (2007) The statistics of gene mapping
- Kang et al. (2010) Variance component model to account for sample structure in genome-wide association studies
- Wu et al. (2009) Genome-wide association analysis by lasso penalized logistic regression
- Alexander and Lange (2011) Stability selection for genome-wide association.
Sequence analysis: alignments and word counts.
- Lecture notes available on Coursework.
Multiple Comparisons in GWAS and genomic studies
- Weights: (1) , (2)
- Separate families of hypotheses: (a) (b)
- Selected families: (*)
- Meta-analysis and replicability: (*)

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CourseWork

Web References

Books

Homework

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