Employing Bayesian inference to calibrate constitutive model parameters has grown substantially in recent years. Among the available techniques, Markov Chain Monte Carlo (MCMC) sampling remains one of the most widely used approaches for estimating the posterior distribution. Nevertheless, the selection of a specific MCMC algorithm is often driven by practical considerations, such as software availability or prior user experience. To support sampler selection, we present a comparison of three prominent samplers in the context of two distinct physical systems: a thermal conduction system and a viscous flow system. Calibration data are obtained through tailor-made experimental setups. We use the Kullback-Leibler (KL) divergence, which quantifies the statistical distance between the sampled posterior and the reference ('true') posterior, as a measure of convergence to compare the performance of the following MCMC sampling methods: the Metropolis-Hastings (MH) sampler, the Affine Invariant Stretch Move (AISM) sampler, and the No-U-Turn Sampler (NUTS). We study how this metric correlates to heuristic indicators such as the Gelman-Rubin diagnostic and the effective sample size. In addition, we assess the samplers' computational effort in terms of required number of model evaluations. Based on the results, we find that the heuristic convergence and performance indicators provide a good qualitative measure for KL-divergence for both systems. Regarding computational effort, the NUTS is net beneficial for the viscous flow system, as the high effective sample size outweighs the additional effort required for gradient-based proposal generation. For the thermal conduction system, which involves more expensive model evaluations, the NUTS is not advantageous. Thus, the computational efficiency of gradient evaluations is an important argument in sampler selection.

翻译：近年来，采用贝叶斯推断校准本构模型参数的实践显著增长。在现有技术中，马尔可夫链蒙特卡洛（MCMC）采样仍是估计后验分布最广泛使用的方法之一。然而，特定MCMC算法的选择往往受实际因素驱动，如软件可用性或个人先验经验。为支持采样器选择，本文在两种不同物理系统（热传导系统和黏性流系统）的背景下比较了三种主流采样器的性能。校准数据通过定制实验装置获取。我们采用量化采样后验与参考（"真实"）后验之间统计距离的库尔贝克-莱布勒（KL）散度作为收敛性指标，比较以下MCMC采样方法的性能：Metropolis-Hastings（MH）采样器、仿射不变拉伸移动（AISM）采样器和无U形转弯采样器（NUTS）。我们研究了该指标与Gelman-Rubin诊断及有效样本量等启发式指标的关联性。此外，我们根据所需模型评估次数评估了各采样器的计算开销。结果表明，两种系统的启发式收敛与性能指标均能为KL散度提供良好的定性度量。就计算开销而言，NUTS在黏性流系统中具有净优势，因其高有效样本量足以抵消梯度建议生成所需的额外计算；而在涉及更昂贵模型评估的热传导系统中，NUTS并无优势。因此，梯度评估的计算效率是采样器选择的重要考量因素。