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

  • Chuanhai Liu
  • Jun Xie
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 164)

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.

Keywords

Monte Carlo Sample Multinomial Distribution Belief Function Probabilistic Inference Inferential Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of StatisticsPurdue UniversityWest LafayetteUSA

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