Parallel generalized elliptical slice sampling with adaptive regional pseudo-priors

MCMC algorithm is well-known for having difficulty exploring distant modes when the target distribution is multi-modal. The reason is that a proposal state is likely to be rejected when traversing across low density regions. Focusing on this issue, we proposed parallel generalized elliptical slice sampling algorithm with adaptive regional pseudo-prior (RGESS). Different from the work of Fagan et al. [2016. Elliptical slice sampling with expectation propagation. In: UAI] and Nishihara et al. [Parallel mcmc with generalized elliptical slice sampling. J Mach Learn Res. 2014;15:2087–2112], different pseudo-priors are used at different regions to conduct the generalized elliptical slice sampling (GESS) algorithm. The rejection rate is modified to guarantee detailed balance condition. We also employ adaptive transition kernel and parallel computing to accelerate sampling speed. Experimental results on one synthetic and one real-world dataset show that the proposed algorithm has the following advantages: with the same starting points, the proposed algorithm spend less time to find the modes of the target distribution; after finding the modes, the proposed algorithm has less interactions between modes due to parameters adaption, which leads to lower rejection rate; when estimating the parameters of multi-modal posterior distributions, the samples generated by proposed algorithm can find different modes better.