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?