  In this paper, we propose a MCMC algorithm based on elliptical slice sampling
with the purpose to improve sampling efficiency. During sampling, a mixture
distribution is fitted periodically to previous samples. The components of the
mixture distribution are called regional pseudo-priors because each component
serves as the pseudo-prior for a subregion of the sampling space. Expectation
maximization algorithm, variational inference algorithm and stochastic
approximation algorithm are used to estimate the parameters. Meanwhile,
parallel computing is used to relieve the burden of computation. Ergodicity of
the proposed algorithm is proven mathematically. Experimental results on one
synthetic and two real-world dataset show that the proposed algorithm has the
following advantages: with the same starting points, the proposed algorithm can
find more distant modes; the proposed algorithm has lower rejection rates; when
doing Bayesian inference for uni-modal posterior distributions, the proposed
algorithm can give more accurate estimations; when doing Bayesian inference for
multi-modal posterior distributions, the proposed algorithm can find different
modes well, and the estimated means of the mixture distribution can provide
additional information for the location of modes.
