Fig. 1.

Open-loop structure of Monte Carlo simulations is enclosed by the gray dashed line. Note that Monte Carlo simulations always draw from the prior distributions, while MCMC simulations draw only from the prior distributions at the first iteration. All subsequent MCMC candidate parameter sets are perturbations of the most recent parameter sets. MCMC simulations directly compare model predictions and experimental data in a closed-loop manner. We built our Markov chains using a Metropolis–Hastings algorithm and single-site updating (see Section II-A for details on the notation).