Abstract
We review three areas of human genetics that have been developed in the past few decades, in which statistical innovation has made a crucial contribution with recent important advances and the potential for further rapid progress. The first topic is the development of mathematical models for the genealogy underlying samples of genome-wide genetic data. Coalescent theory emerged in the 1980s, leaped ahead in the past decade and is now burgeoning into new application areas in population, evolutionary and medical genetics. The second is the development of statistical methods for genome-wide association studies which has made great strides over two decades, including exciting recent developments for association testing based on coalescent theory and improved methods for trait prediction. Finally, we review the statistical ideas that helped resolve the controversies surrounding the introduction of forensic DNA profiling in the early 1990s. Big advances in interpretation of the predominant autosomal DNA profiles have set a benchmark for other areas of forensic science, but the statistical assessment of uniparentally inherited profiles (derived from the mitochondrial DNA or the Y chromosome) remains unsatisfactory.