I am after some general advice regarding my MCMC scheme, which is causing me some grief.
Essentially, I have a large (2N + 9 parameters) MCMC scheme which works great. However, the problem is that the estimation of two of these parameters consumes around 95% of the total computational time. The sampler can take up to 25 hours to sample (large data set @ 20,000 sweeps).
However, for these two special parameters, once they are estimated (after 1,000 loops or so), they are estimated very accurately, and do not move much (extremely small bias). Clearly, there is no benefit to estimate these parameters for each sweep, as they are time consuming and do not change very much.
Is there an "elegant" way to avoid having to estimate these parameters for each sweep? Is there examples where people estimate it for say, every 10th sweep? Not sure if by doing this, it will violate some serious Markov chain assumptions. Thanks in advance for any tips you can provide.
Edit: Without going into too much unnecessary detail, my model is hierarchical, and these two particular parameters are estimated jointly.