Next-Generation Statistical Genetics: Modeling, Penalization, and Optimization in High-Dimensional Data

Statistical genetics is undergoing the same transition to big data that all branches of applied statistics are experiencing, and this transition is only accelerating with the advent of inexpensive DNA sequencing technology. This brief review highlights some modern techniques with recent successes in statistical genetics. These include (a) Lasso penalized regression for association mapping, (b) ethnic admixture estimation, (c) matrix completion for genotype and sequence imputation, (d) the fused Lasso for discovery of copy number variation, (e) haplotyping, (f) relatedness estimation, (g) variance components models, and (h) rare variant testing. For more than a century, genetics has been both a driver and beneficiary of statistical theory and practice. This symbiotic relationship will persist for the foreseeable future.