The estimation of individual ancestry from genetic data has become essential to applied population genetics and genetic epidemiology. Software programs for calculating ancestry estimates have become essential tools in the geneticist's analytic arsenal.

Motivation: In ordinary regression, imposition of a lasso penalty makes continuous model selection straightforward. Lasso penalized regression is particularly advantageous when the number of predictors far exceeds the number of observations.Method: The present article evaluates the performance of lasso penalized logistic regression in case–control disease gene mapping with a large number of SNPs (single nucleotide polymorphisms) predictors. The strength of the lasso penalty can be tuned to select a predetermined number of the most relevant SNPs and other predictors. For a given value of the tuning constant, the penalized likelihood is quickly maximized by cyclic coordinate ascent. Once the most potent marginal predictors are identified, their two-way and higher order interactions can also be examined by lasso penalized logistic regression.Results: This strategy is tested on both simulated and real data. Our findings on coeliac disease replicate the previous SNP results and shed light on possible interactions among the SNPs.Availability: The software discussed is available in Mendel 9.0 at the UCLA Human Genetics web site.Contact: klange@ucla.eduSupplementary information: Supplementary data are available at Bioinformatics online.

Clustering is a fundamental problem in many scientific applications. Standard methods such as k-means, Gaussian mixture models, and hierarchical clustering, however, are beset by local minima, which are sometimes drastically suboptimal. Recently introduced convex relaxations of k-means and hierarchical clustering shrink cluster centroids toward one another and ensure a unique global minimizer. In this work, we present two splitting methods for solving the convex clustering problem. The first is an instance of the alternating direction method of multipliers (ADMM); the second is an instance of the alternating minimization algorithm (AMA). In contrast to previously considered algorithms, our ADMM and AMA formulations provide simple and unified frameworks for solving the convex clustering problem under the previously studied norms and open the door to potentially novel norms. We demonstrate the performance of our algorithm on both simulated and real data examples. While the differences between the two algorithms appear to be minor on the surface, complexity analysis and numerical experiments show AMA to be significantly more efficient. This article has supplementary materials available online.

Summary: Mendel is one of the few statistical genetics packages that provide a full spectrum of gene mapping methods, ranging from parametric linkage in large pedigrees to genome-wide association with rare variants. Our latest additions to Mendel anticipate and respond to the needs of the genetics community. Compared with earlier versions, Mendel is faster and easier to use and has a wider range of applications. Supported platforms include Linux, MacOS and Windows. Availability: Free from www.genetics.ucla.edu/software/mendel Contact:klange@ucla.edu Supplementary information: Supplementary data are available at Bioinformatics online.

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.