Pitfalls and Opportunities in the Use of Markov-Chain Monte Carlo Ensemble Samplers for Vadose Zone Model Calibration

Bayesian inference has become the most popular approach to uncertainty assessment in vadose zone hydrological modeling. By combining prior information with observations and model predictions, it became popular among hydrologists as it enables them to infer parameter posterior distributions, verify model adequacy, and assess the model's predictive uncertainty. In particular, the posterior distribution is frequently the variable of interest for modelers as it describes the epistemic uncertainty of model parameters conditioned on measurements. Gradient-free Markov-Chain Monte Carlo (MCMC) ensemble samplers based on Differential Evolution (DE) or Affine Invariant (AI) strategies have been used to approximate the posterior distribution, which is frequently anisotropic and correlated in vadose zone-related problems. However, a rigorous benchmark of different MCMC algorithms to provide guidelines for their application in vadose zone hydrological model calibration is still missing. In this study, we elucidate the behavior of MCMC ensemble samplers by performing an in-depth comparison of four samplers that use AI moves or DE-based strategies to approximate the target density. Two Rosenbrock distributions, and one synthetic and one actual case study focusing on the inverse estimation of soil hydraulic parameters using HYDRUS-1D, are used to compare algorithms in different dimensions. The analysis reveals that AI-based samplers are immune to affine transformations of the target density, which instead double the autocorrelation time for DE-based samplers. This behavior is reiterated in the synthetic scenario, for which AI-based algorithms outperform DE-based strategies. However, this performance gain disappears when the number of soil parameters increases from 7 to 16, with both samplers exhibiting poor acceptance rates, which are not improved by increasing the number of chains from 50 to 200 or by mixing different strategies.