  We propose a novel class of Sequential Monte Carlo (SMC) algorithms,
appropriate for inference in probabilistic graphical models. This class of
algorithms adopts a divide-and-conquer approach based upon an auxiliary
tree-structured decomposition of the model of interest, turning the overall
inferential task into a collection of recursively solved sub-problems. The
proposed method is applicable to a broad class of probabilistic graphical
models, including models with loops. Unlike a standard SMC sampler, the
proposed Divide-and-Conquer SMC employs multiple independent populations of
weighted particles, which are resampled, merged, and propagated as the method
progresses. We illustrate empirically that this approach can outperform
standard methods in terms of the accuracy of the posterior expectation and
marginal likelihood approximations. Divide-and-Conquer SMC also opens up novel
parallel implementation options and the possibility of concentrating the
computational effort on the most challenging sub-problems. We demonstrate its
performance on a Markov random field and on a hierarchical logistic regression
problem.
