  For Bayesian computation in big data contexts, the divide-and-conquer MCMC
concept splits the whole data set into batches, runs MCMC algorithms separately
over each batch to produce samples of parameters, and combines them to produce
an approximation of the target distribution. In this article, we embed random
forests into this framework and use each subposterior/partial-posterior as a
proposal distribution to implement importance sampling. Unlike the existing
divide-and-conquer MCMC, our methods are based on scaled subposteriors, whose
scale factors are not necessarily restricted to being equal to one or to the
number of subsets. Through several experiments, we show that our methods work
well with models ranging from Gaussian cases to strongly non-Gaussian cases,
and include model misspecification.
