Propriety of posterior in Bayesian space varying parameter models with normal data

Network-based genomic discovery: application and comparison of Markov random field models

As biological knowledge accumulates rapidly, gene networks encoding genome-wide gene-gene interactions have been constructed. As an improvement over the standard mixture model that tests all the genes iid a priori, Wei and Li (2007) and Wei and Pan (2008) proposed modeling a gene network as a Discrete- or Gaussian-Markov random field (DMRF or GMRF) respectively in a mixture model to analyze genomic data. However, how these methods compare in practical applications in not well understood and this is the aim here. We also propose two novel constraints in prior specifications for the GMRF model and a fully Bayesian approach to the DMRF model. We assess the accuracy of estimating the False Discovery Rate (FDR) by posterior probabilities in the context of MRF models. Applications to a ChIP-chip data set and simulated data show that the modified GMRF models has superior performance as compared with other models, while both MRF-based mixture models, with reasonable robustness to misspecified gene networks, outperform the standard mixture model.