A Comparison of MCMC Algorithms for an Inverse Squeeze Flow Problem

Using Bayesian inference to calibrate constitutive model parameters has recently seen a rise in interest. The Markov chain Monte Carlo (MCMC) algorithm is one of the most commonly used methods to sample from the posterior. However, the choice of which MCMC algorithm to apply is typically pragmatic and based on considerations such as software availability and experience. We compare three commonly used MCMC algorithms: Metropolis-Hastings (MH), Affine Invariant Stretch Move (AISM) and No-U-Turn sampler (NUTS). For the comparison, we use the Kullback-Leibler (KL) divergence as a convergence criterion, which measures the statistical distance between the sampled and the ‘true’ posterior. We apply the Bayesian framework to a Newtonian squeeze flow problem, for which there exists an analytical model. Furthermore, we have collected experimental data using a tailored setup. The ground truth for the posterior is obtained by evaluating it on a uniform reference grid. We conclude that, for the same number of samples, the NUTS results in the lowest KL divergence, followed by the AISM sampler and last the MH sampler.