  This paper presents Sparse Partitioning, a Bayesian method for identifying
predictors that either individually or in combination with others affect a
response variable. The method is designed for regression problems involving
binary or tertiary predictors and allows the number of predictors to exceed the
size of the sample, two properties which make it well suited for association
studies. Sparse Partitioning differs from other regression methods by placing
no restrictions on how the predictors may influence the response. To compensate
for this generality, Sparse Partitioning implements a novel way of exploring
the model space. It searches for high posterior probability partitions of the
predictor set, where each partition defines groups of predictors that jointly
influence the response. The result is a robust method that requires no prior
knowledge of the true predictor--response relationship. Testing on simulated
data suggests Sparse Partitioning will typically match the performance of an
existing method on a data set which obeys the existing method's model
assumptions. When these assumptions are violated, Sparse Partitioning will
generally offer superior performance.
