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I am running a MCMC Gibbs sampler for a computationally expensive model. It takes ~12 hours to obtain 1000 iterations of this MCMC sampler. I have tested the sampler, and I found that the chain seems to have converged after 2000 iterations (1 day). So, I am planning to use the last point of this chain as a new initial point in order to run 10 chains in parallel (using different seeds) with this initial point, in order to reduce the running time. So I will end up with 10,000 posterior samples in a tenth of the time.

Is this a valid approach?

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I would rather not suggest this course of action since, all chains starting from the very same point, $X^{(2000)}$ say, these chains need run long enough to cancel the dependence on that starting point and recover simulations from the target. For instance, if one removes some burnin part (20%? 50%?) from all 10 parallel chains, this would come closer to a set of 10 independent MCMC samples run under the stationary distribution. But

  1. the pooled outcome of the ten chains cannot be deemed as an iid sample for (a) the intra-chain dependence and (b) the possible omission of one part of the target by all chains (in case of non-geometric convergence).

  2. starting at iteration one with 10 parallel chains and a highly dispersed stating distribution would provide more realisations and henceopen the possibility of subsampling with wider gaps towards a better approximation of iid sampling.

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