Michele Guindani
Department of Mathematics and Statistics
University of New Mexico
A Bayesian Discovery Procedure
We discuss a Bayesian discovery procedure for multiple-comparison problems.
We show that, under a coherent decision theoretic framework, a loss function
combining true positive and false positive counts leads to a decision rule
that is based on a threshold of the posterior probability of the
alternative. Under a semiparametric model for the data, we show that the
Bayes rule can be approximated by the optimal discovery procedure, which was
recently introduced by Storey (2007). Improving the approximation leads us
to a Bayesian discovery procedure, which exploits the multiple shrinkage in
clusters that are implied by the assumed non-parametric model. We
compare the Bayesian discovery procedure and the optimal discovery procedure
estimates in a simple simulation study and in an assessment of differential
gene expression based on microarray data from tumor samples. We extend the
setting of the optimal discovery procedure by discussing modifications of
the loss function that lead to different single-thresholding statistics.
Finally, we provide an application of the previous arguments to spatial
data. Most of this presentation stems from a joint work with Peter Muller
and Song Zhang.
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