Likelihood-ratio propagation and consensus in wireless networks with Markov Random Field models

In this paper we address the problem of distributed Bayesian hypothesis testing in wireless networks where correlations among nodes are modeled as exponential Markov Random Fields (MRF). Applying distributed Belief Propagation (BP), we first derive message and belief update rules for the above model expressed under a likelihood ratio formulation. Then we analyze the properties of BP when the MRF correlation values tend to infinity, and we show that in this limit BP behaves as a consensus scheme. As a result, both problems of heterogeneous hypothesis testing (i.e., MRF estimation) and homogeneous hypothesis testing (i.e., consensus building) can be seen under a unified framework.