Bayesian reliability-based prediction of the soil water retention curve using finite data

The soil water retention curve (SWRC) is a core concept of unsaturated soil mechanics. To date, while various SWRC prediction models have been developed, they require large datasets to generate accurate results. Most importantly, and uncoincidentally, obtaining large SWRC datasets from experimental procedures might prove costly, time-consuming, and sometimes rigorous; thus, making only limited data available for use. However, determining the inherent uncertainties in predictions when using finite data has been elusive. To address this problem, we propose a reliability-based approach using a Bayesian framework that is logical and rigorous for quantifying uncertainty in model parameters. The proposed Bayesian method is Hamiltonian Monte Carlo (HMC). The HMC is a Markov chain Monte Carlo (MCMC) method that applies the Hamiltonian dynamics to solve and update posterior distributions in Bayesian analysis. Different SWRC datasets and models were used to validate and test the efficacy and robustness of the model in making predictions. The results show that the method is so robust that even imperfect prior knowledge provides reliable SWRC prediction results comparable with other methods. Furthermore, computation time and cost are significantly reduced because of the small (MCMC) sample size required to complete numerical solutions.