  High-throughput scientific studies involving no clear a'priori hypothesis are
common. For example, a large-scale genomic study of a disease may examine
thousands of genes without hypothesizing that any specific gene is responsible
for the disease. In these studies, the objective is to explore a large number
of possible factors (e.g. genes) in order to identify a small number that will
be considered in follow-up studies that tend to be more thorough and on smaller
scales. For large-scale studies, we propose a nonparametric Bayesian approach
based on random partition models. Our model thus divides the set of candidate
factors into several subgroups according to their degrees of relevance, or
potential effect, in relation to the outcome of interest. The model allows for
a latent rank to be assigned to each factor according to the overall potential
importance of its corresponding group. The posterior expectation or mode of
these ranks is used to set up a threshold for selecting potentially relevant
factors. Using simulated data, we demonstrate that our approach could be quite
effective in finding relevant genes compared to several alternative methods. We
apply our model to two large-scale studies. The first study involves
transcriptome analysis of infection by human cytomegalovirus (HCMV). The
objective of the second study is to identify differentially expressed genes
between two types of leukemia.
