Large-Scale Multinomial Inference and Its Applications in Genome-Wide Association Studies

研究者研究了大量K个类别和少量n个样本量的多项式计数的统计分析。这个“大K小n”的问题是一个非常具有挑战性的问题，需要在基本层面上思考统计推断。pi采用辅助数据生成方法直接对概率推理进行推理，开发了概率性和具有理想频率特性的方法。要研究的一系列主题包括：1)单样本和双样本“大K小n”多项式推理；2)大规模同时假设检验；3)在全基因组关联研究中的应用；4)相关的高效计算方法。“大K小n”的多项推断是由来自单核苷酸多态性（SNPs）数据的大量基因型的全基因组关联研究推动的。snp是主要的基因变异，可能与癌症和心脏病等常见疾病有关。随着新统计方法和计算软件的开发，该研究有望为应用统计学家和科学家提供有用的工具，这些统计学家和科学家面临着非常高维计数数据的挑战。

The investigators study statistical analysis of multinomial counts with alarge number K of categories and a small number n of sample size. This"large K and small n" problem is a very challenging problem that requires thinking about statistical inference at a fundamental level. Employing an auxiliary data-generating approach to reason directly toward probabilistic inference , the PIs develop methods that are probabilistic and have desirable frequency properties. A sequence of topics to be investigated include 1) one-sample and two-sample "large K and small n" multinomial inference; 2) large-scale simultaneous hypothesis testing; 3) application in genome-wide association study; and 4) associated efficient computational methods. The "large K and small n" multinomial inference is motivated by genome-wideassociation studies with a large number of genotypes from singlenucleotide polymorphisms (SNPs) data. SNPs are major genetic variants that mayassociate with common diseases such as cancer and heart disease. With new statistical methods and computing software to be developed in the project, theresearch is expected to generate useful tools for applied statisticians andscientists who are challenged by very-high-dimensional count data.