I have been reading about model counting, a.k.a. the #SAT problem. What are the practical applications, if any, of this problem, and how exactly do they reduce to it? I have been unable to find any, though that's simply due to my own ignorance of the subject.
A recurring application for SAT model counting in the literature is extracting predictions from Bayesian networks. See "Algorithms and Complexity Results for #SAT and Bayesian Inference" and "On probabilistic inference by weighted model counting".