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In this paper, we propose a MCMC algorithm based on elliptical slice samplingwith the purpose to improve sampling efficiency. During sampling, a mixturedistribution is fitted periodically to previous samples. The components of themixture distribution are called regional pseudo-priors because each componentserves as the pseudo-prior for a subregion of the sampling space. Expectationmaximization algorithm, variational inference algorithm and stochasticapproximation algorithm are used to estimate the parameters. Meanwhile,parallel computing is used to relieve the burden of computation. Ergodicity ofthe proposed algorithm is proven mathematically. Experimental results on onesynthetic and two real-world dataset show that the proposed algorithm has thefollowing advantages: with the same starting points, the proposed algorithm canfind more distant modes; the proposed algorithm has lower rejection rates; whendoing Bayesian inference for uni-modal posterior distributions, the proposedalgorithm can give more accurate estimations; when doing Bayesian inference formulti-modal posterior distributions, the proposed algorithm can find differentmodes well, and the estimated means of the mixture distribution can provideadditional information for the location of modes.

Generalized Elliptical Slice Sampling with Regional Pseudo-priors