  We develop a model-based methodology for integrating gene-set information
with an experimentally-derived gene list. The methodology uses a previously
reported sampling model, but takes advantage of natural constraints in the
high-dimensional discrete parameter space in order to work from a more
structured prior distribution than is currently available. We show how the
natural constraints are expressed in terms of linear inequality constraints
within a set of binary latent variables. Further, the currently available prior
gives low probability to these constraints in complex systems, such as Gene
Ontology (GO), thus reducing the efficiency of statistical inference. We
develop two computational advances to enable posterior inference within the
constrained parameter space: one using integer linear programming for
optimization and one using a penalized Markov chain sampler. Numerical
experiments demonstrate the utility of the new methodology for a multivariate
integration of genomic data with GO or related information systems. Compared to
available methods, the proposed multi-functional analyzer covers more reported
genes without mis-covering nonreported genes, as demonstrated on genome-wide
data from association studies of type 2 diabetes and from RNA interference
studies of influenza.
