  Given a multiple testing situation, the null hypotheses that appear to have
sufficiently low probabilities of truth may be rejected using a simple,
nonparametric method of decision theory. This applies not only to posterior
levels of belief, but also to conditional probabilities in the sense of
relative frequencies, as seen from their equality to local false discovery
rates (dFDRs). This approach neither requires the estimation of probability
densities, nor of their ratios. Decision theory can inform the selection of
false discovery rate weights. Decision theory is applied to gene expression
microarrays with discussion of the applicability of the assumption of weak
dependence.
