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

Summary. As biological knowledge accumulates rapidly, gene networks encoding genomewide gene–gene interactions have been constructed. As an improvement over the standard mixture model that tests all the genes identically and independently distributed a priori, Wei and co‐workers have proposed modelling a gene network as a discrete or Gaussian Markov random field (MRF) in a mixture model to analyse genomic data. However, how these methods compare in practical applications is not well understood and this is the aim here. We also propose two novel constraints in prior specifications for the Gaussian MRF model and a fully Bayesian approach to the discrete MRF model. We assess the accuracy of estimating the false discovery rate by posterior probabilities in the context of MRF models. Applications to a chromatin immuno‐precipitation–chip data set and simulated data show that the modified Gaussian MRF models have superior performance compared with other models, and both MRF‐based mixture models, with reasonable robustness to misspecified gene networks, outperform the standard mixture model.