A Comparison of MCMC Algorithms for the Bayesian Calibration of Building Energy Models

Abstract

Random walk Metropolis and Gibbs sampling are Markov Chain Monte Carlo (MCMC) algorithms that are typically used for the Bayesian calibration of building energy models. However, these algorithms can be challenging to tune and achieve convergence when there is a large number of parameters. An alternative sampling method is Hamiltonian Monte Carlo (HMC) whose properties allow it to avoid the random walk behavior and converge to the target distribution more easily in complicated high-dimensional problems. Using a case study, we evaluate the effectiveness of three MCMC algorithms: (1) random walk Metropolis, (2) Gibbs sampling and (3) No-UTurn Sampler (NUTS) (Hoffman and Gelman, 2014), an extension of HMC. The evaluation was carried out using a Bayesian approach that follows Kennedy and O’Hagan (2001). We combine field and simulation data using the statistical formulation developed by Higdon et al. (2004). It was found that NUTS is more effective for the Bayesian calibration of building energy models as compared to random walk Metropolis and Gibbs sampling