Abstract
In this paper, by the novel idea of integrating multiple-proposal algorithm and multiple-chain algorithm by parallel computing, we develop a highly efficient sampler for approximating statistical distributions: parallel Multi-proposal and Multi-chain Markov Chain Monte Carlo (pMPMC3), and we illustrate the high performance of this sampler by calculating P-value (odds ratio significance) for Genome Wide Association Study (GWAS). Computational results show that, by setting the convergence condition as the standard deviation of P-value is less than 10−3, pMPMC3 with 4 proposals and 4 chains obtains a convergent P-value within 106 iterations, while the conventional method Monte Carlo simulation does not obtain convergent P-values even in 107 iterations. We also test pMPMC3 by changing the number of chains, the number of proposals and the size of the dataset on a cluster with maximum 600 processes, the algorithm scales well.
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