Statistical methods for large-scale inference

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As the high-throughput technologies are increasingly adopted in practice, large-scale statistical inference is commonly conducted in many scientific research areas, including genetic, neuroimaging, astronomy, and many others. More specifically, in genome-wide association studies (GWAS) or neuroimaging studies, we need to conduct millions of hypothesis tests simultaneously, each of which concerns whether a single nucleotide polymorphism (SNP) or voxel is associated with a phenotype, respectively. The challenge of simultaneously testing many hypotheses is commonly referred to as the multiple testing problem. This proposal is mainly motivated by the realization that scientific investigations are rarely conducted in isolation, and there are typically relevant information and related experiments in the literature. For example, the summary statistics from a related disease can be highly informative for the inference of a target disease. Traditional multiple testing methods do not consider the relevant auxiliary information. In this proposal, we intend to develop powerful multiple testing methods by utilizing the auxiliary information while maintaining proper error control. The statistical methods developed can accelerate the progress of scientific discoveries by allowing scientists to fully utilize existing auxiliary information. We also plan to develop powerful methods to analyze GWAS by taking advantage of the correlations among test statistics. The applications of our methods can advance our understanding of the genetic basis of many human complex traits and diseases, including height, obesity, rheumatic diseases, developmental disorders, and many others.