  This note provides a detailed description and derivation of the domain
decomposition algorithm that appears in previous works by the author. Given a
large re-estimation problem, domain decomposition provides an iterative method
for assembling Boltzmann distributions associated to small subproblems into an
approximation of the Bayesian posterior of the whole problem. The algorithm is
amenable to using Boltzmann sampling to approximate these Boltzmann
distributions. In previous work, we have shown the capability of heuristic
versions of this algorithm to solve LDPC decoding and circuit fault diagnosis
problems too large to fit on quantum annealing hardware used for sampling.
Here, we rigorously prove soundness of the method.
