The use of Bayesian methods in genetics has a long history. This introductory module begins by discussing introductory probability. It then describes Bayesian approaches to binomial proportions, multinomial proportions, two-sample comparisons (binomial, Poisson, normal), the linear model, and Monte Carlo methods of summarization. Advanced topics include hierarchical models, generalized linear models, and missing data. Illustrative applications will include: Hardy-Weinberg testing and estimation, detection of allele-specific expression, QTL mapping, testing in genome-wide association studies, mixture models, multiple testing in high throughput genomics.

Suggested pairing: Module 8: Statistical Genetics

Learning Objectives: After attending this module, participants will be able to:

1. Understand the roles, in principle, of Bayesian analysis of prior, likelihood and posterior, and how these differ from default frequentist approaches.
2. Apply these principles to simple conjugate analyses, e.g. beta-binomial, Dirichlet-multinomial and Normal-Normal, interpreting their output in analysis of genetic data.
3. Understand the principles of how numeric calculations are done to evaluate the posterior in low and fixed-dimensional modeling, including MCMC and INLA.
4. Use standard packages to implement MCMC and INLA-based analysis of low and fixed-dimensional problems, emphasizing their use in genetic analyses.
5. Understand Bayesian interpretations/justifications for multiple testing, with application to high-throughput genetics.
6. Understand Bayesian interpretations/justifications for model-averaging, with application to genetic analyses.

Understand Bayesian interpretations/justifications for meta-analysis and other forms of evidence synthesis, with application to genetic analyses.