|
Abstract:
|
Multiple hypothesis testing arises in areas as diverse as epidemiology, brain imaging, genomics, and clinical trials, with perhaps the canonical example being DNA microarrays. The standard Bayesian parametric approach is to assume that all hypotheses are independently true or false with a common prior inclusion probability p, which is itself a model parameter to be estimated. This induces shrinkage of all posterior inclusion probabilities toward the posterior mean of p, yielding an automatic penalty for testing more hypotheses. This paper considers extensions of this model to general variable selection problems by relaxing the assumption of independence. We also describe a stochastic search algorithm for exploring the resulting high-dimensional model space, and we recommend prior distributions for model parameters that dovetail nicely with the search strategy.
|
