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Published in:
2012 | OriginalPaper | Chapter
Large Scale Multinomial Inferences and Its Applications in Genome Wide Association Studies
Authors : Chuanhai Liu, Jun Xie
Published in: Belief Functions: Theory and Applications
Publisher: Springer Berlin Heidelberg
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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.