High-dimensional statistics, with applications to genome-wide association studies

Abstract

We present a selective review on high-dimensional statistics where the dimensionality of the unknown parameter in a model can be much larger than the sample size in a dataset (e.g. the number of people in a study). Particular attention is given to recent developments for quantifying uncertainty in high-dimensional scenarios. Assessing statistical uncertainties enables to describe some degree of replicability of scientific findings, an ingredient of key importance for many applications. We also show here how modern high-dimensional statistics offers new perspectives in an important area in genetics: novel ways of analyzing genome-wide association studies, towards inferring more causal-oriented conclusions.