Large Scale Multinomial Inferences and Its Applications in Genome Wide Association Studies

Abstract

Statistical analysis of multinomial counts with a large number K of categories and a small number n of sample size is challenging to both frequentist and Bayesian methods and requires thinking about statistical inference at a very fundamental level. Following the framework of Dempster-Shafer theory of belief functions, a probabilistic inferential model is proposed for this “large K and small n” problem. Using a data-generating device, the inferential model produces probability triplet (p,q,r) for an assertion conditional on observed data. The probabilities p and q are for and against the truth of the assertion, whereas r = 1- p − q is the remaining probability called the probability of “don’t know”. The new inference method is applied in a genome-wide association study with very-high-dimensional count data, to identify association between genetic variants to a disease Rheumatoid Arthritis.