We consider performing Markov Chain Monte Carlo in parallel. We present an algorithm for sampling random variables which allows us to divide the sampling-process into sub- problems by dividing the sample space into overlapping parts. The sub-problems can be solved independently of each other and are thus well suited for parallelization. Further, on each of these sub-problems we can use distinct and independent sampling methods. In other words, we can design specific samplers for specific parts of the sample space. Moreover we present an algorithm which parallelizes the Metropolis-Hastings algorithm up to the point where it is as fast as it would be with 100%-acceptance rate. The algorithms are demonstrated on a particle marginal Metropolis-Hastings-sampler applied to calibration of a volatility model.
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