  By mixing the target posterior distribution with a surrogate distribution, of
which the normalizing constant is tractable, we propose a method for estimating
the marginal likelihood using the Wang-Landau algorithm. We show that a faster
convergence of the proposed method can be achieved via the momentum
acceleration. Two implementation strategies are detailed: (i) facilitating
global jumps between the posterior and surrogate distributions via the
Multiple-try Metropolis; (ii) constructing the surrogate via the variational
approximation. When a surrogate is difficult to come by, we describe a new
jumping mechanism for general reversible jump Markov chain Monte Carlo
algorithms, which combines the Multiple-try Metropolis and a directional
sampling algorithm. We illustrate the proposed methods on several statistical
models, including the Log-Gaussian Cox process, the Bayesian Lasso, the
logistic regression, and the g-prior Bayesian variable selection.
