We consider the problem of identifying a pattern of faults from a 
set of noisy linear measurements. Unfortunately, maximum a posteriori 
probability estimation of the fault pattern is computationally 
intractable. To solve the fault identification problem, we propose 
a non-parametric belief propagation approach, which is related to 
recent compressed sensing algorithms. We show that our belief 
propagation solver is more accurate than recent state-of-the-art 
algorithms. Our superior performance is explained by the fact that 
we take into account both the binary nature of the individual faults 
and the sparsity of the fault pattern arising from their rarity.