Statistical Modelling 8 (2008), 23–39
Simultaneous inference for multiple testing and clustering via a
Dirichlet process mixture model
David B Dahl
Department of Statistics,
Texas A&M University,
College Station, TX 77843
USA
eMail:
dahl@state.tamu.edu
Qianxing Mo
Memorial Sloan-Kettering Cancer Center
USA
Marina Vannucci
Rice University
USA
Abstract:
We propose a Bayesian nonparametric regression model that exploits
clustering for increased sensitivity in multiple hypothesis testing.
We build on the recently proposed BEMMA (Bayesian Effects Models for
Microarrays) method which is able to model dependence among objects
through clustering and then estimates hypothesis-testing parameters
averaged over clustering uncertainty. We propose several improvements.
First, we separate the clustering of the regression coefficients from
the part of the model that accommodates heteroscedasticity. Second,
our model accommodates a wider class of experimental designs, such as
permitting covariates and not requiring independent sampling. Third,
we provide a more satisfactory treatment of nuisance parameters and
some hyperparameters. Finally, we do not require the arbitrary
designation of a reference treatment. The proposed method is compared
in a simulation study to ANOVA and the BEMMA methods.
Keywords:
Bayesian nonparametrics; correlated hypothesis tests;
model-based clustering; multiple comparisons
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