An in-depth analysis of Markov-Chain Monte Carlo ensemble samplers for inverse vadose zone modeling

• Published in: Journal of hydrology (Amsterdam) 2023-09, Vol.624, p.129822, Article 129822
• Main Authors: Brunetti, Giuseppe, Šimunek, Jiri, Wöhling, Thomas, Stumpp, Christine
• Format: Article
• Language: English
• Subjects: Affine invariant; Differential evolution; Ensemble samplers; Markov-chain Monte Carlo; Vadose zone
• ISSN: 0022-1694; 1879-2707
• DOI: 10.1016/j.jhydrol.2023.129822

This study elucidates the behavior of Markov-Chains Monte Carlo ensemble samplers for vadose zone inverse modeling by performing an in-depth comparison of four algorithms that use Affine-Invariant (AI) moves or Differential Evolution (DE) strategies to approximate the target density. Two Rosenbrock toy 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 samplers in different dimensions d. The analysis reveals that an ensemble with N=d+1 chains evolved using DE-based strategies converges to the wrong stationary posterior, while AI does not suffer from this issue but exhibits delayed convergence. DE-based samplers regain their ergodic properties when using N≥2d chains. Increasing the number of chains above this threshold has only minor effects on the samplers’ performance, while initializing the ensemble in a high-likelihood region facilitates its convergence. AI strategies exhibit shorter autocorrelation times in the 7d synthetic vadose zone scenario, while DE-based samplers outperform them when the number of soil parameters increases to 16 in the actual scenario. All evaluation metrics degrade as d increases, thus suggesting that sampling strategies based only on interpolation between chains tend to become inefficient when the bulk of the posterior lays in increasingly small portions of the parameters’ space. •Affine-Invariant (AI) and Differential Evolution (DE) strategies are compared.•DE samplers converge to the wrong posterior if the number of chains N is low.•It is advisable to increase N and start the ensemble in a high-likelihood region.•AI outperforms DE for low dimensional vadose zone problems.•DE shows better performance when the number of parameters increases.