Bayesian Methods in Fisher’s Statistical Genetics World

Statistical genetics is a scientific discipline that covers any statistical analysis of genetic data. The interplay between statistics and genetics has a long history, dating back to the seminal work by Fisher almost a century ago to confirm the genetic theory of chromosomal inheritance (Piegorsch, 1990). Recent advancements in genotyping (i.e., collecting genetic data) technologies have produced vast amounts of data, offering statisticians great opportunities in methodological development, implementation and application. For example , the high-dimensional genome-wide association studies conducted in the last few years have led to the development of a catalog of novel statistical methods for dissecting the genetic architecture of complex human traits; see, e.g., Thomas et al. (2009) and Begum et al. (2012). The types of genetic data available are quite diverse; they include micro-satellites, single-nucleotide polymorphisms, copy number variations, DNA methylation, and gene expression. The corresponding statistical methodolo-gies are equally diverse, as illustrated by Bull et al. in Chapter 8. For clarity and a more focused discussion, this expository piece is centered around studies of genetic association between single-nucleotide polymorphisms and heritable human traits. In the following, we first provide relevant genetic terminology. We then formulate genetic association studies in terms of regression models in which inferences on the regression coefficients are of interest. Using a published genome-wide association study as an example, we first describe the commonly used frequentist approaches to achieve testing and estimation objectives, and we then discuss alternative Bayesian methods and associated advantages as well as challenges. We conclude with discussions of other recent developments in Bayesian statistical genetics, focusing on contributions made by Canadian statisticians, and comment on future directions.