Preconditioned Metropolis sampling as a strategy to improve efficiency in Posterior exploration*

In this paper we look at the problem from the perspective of the Markov chain Monte Carlo method. Assuming the existence of a practically exact, but expensive, master equations solver, together with a cheaper, approximate alternative, we pick up the idea of preconditioned Metropolis sampling. Here the solutions of full master equations almost always imply an accepted step in the Markov chain, and consequently, step rejections are much cheaper. We investigate the properties of this technique theoretically and via illustrative examples. Whenever a suitable preconditioner is available, large savings in computational times are possible while the accuracy in deduced parameters is identical to using the exact likelihood.