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Marginal likelihood (or Bayesian evidence) estimation is the basis for model evaluation and model selection, which is the key research content of the uncertainty quantification of groundwater model structure. Recently, the nested sampling estimator (NSE) has been widely used as an efficient method to estimate the marginal likelihood. The Metropolis-Hasting (M-H) algorithm is usually used to explore the model likelihood space for NSE. However, M-H is inefficient in searching complex likelihood functions, especially for the multimodal distribution functions, because of the sampling structure of M-H algorithm. The multi-try differential evolution adaptive Metropolis (MT-DREAMzs) algorithm is effective and robust in searching complex probability space, and it is incorporated into NSE to improve the performance of marginal likelihood estimation in this study. In addition, the developed MT-DREAMzs-based NSE (NSE_MT) is evaluated by comparing with several other marginal likelihood estimators including DREAMzs-based and M-H-based NSEs (NSE_DR, NSE_MH), Gaussian mixture importance (GAME) sampling and a new nested sampling algorithm (PolyChord). Based on three analytical functions (up to 100 dimensions) and one groundwater solute transport case studies, the results showed that NSE_MT outperforms NSE_MH in the convergence, efficiency and accuracy of marginal estimation, and NSE_MT is slightly more efficient and accurate than NSE_DR. The accuracy of NSE_MH, NSE_DR and NSE_MT deteriorates with increasing dimensionality of target distributions/model parameters. In addition, GAME sampling and PolyChord sampling outperform other three NSEs in the accuracy and stability of estimation for high dimensional (up to 100-variate) distributions, and PolyChord is slightly less accurate and stable than GAME. Compared with GAME and PolyChord, NSE_MT and NSE_DR are competent for less than 10-dimensional distributions with higher computational efficiency. [ABSTRACT FROM AUTHOR]

• Nine GPR kernels are evaluated in improving groundwater model prediction. • GPR kernel has apparent influence on capturing systematic prediction error. • The single kernel RQ has the best performance in improving groundwater prediction. Systematic model error is caused by the unreasonable simplification of real groundwater system, which damages the reliability of groundwater model prediction. Gaussian process regression (GPR) is a popular data-driven method used to build a statistical complementary model to correct systematic prediction error and improve model prediction. Kernel function is a crucial component of GPR, it represents the assumptions on systematic prediction error that we want to learn. In order to evaluate the influence of GPR kernel on capturing systematic prediction error, we compared the performances of GPR with nine kernels in groundwater predictions. These kernels include three commonly used single kernels, i.e., squared exponential (SE), Matérn class (MT), and rational quadratic (RQ) kernels, and six new kernels formed by combining these single kernels as sum or product of pairs (SE_MT_s, SE_RQ_s, MT_RQ_s, SE_MT_p, SE_RQ_p, and MT_RQ_p). Moreover, three groundwater case studies, including two analytical cases and one real case, are used to test these kernels, and four metrics are applied to measure the performances of these kernels. The evaluation results show that kernel functions have apparent influence on the ability of the GPR-based complementary model to capture the systematic prediction error of groundwater model. The single kernel RQ-based GPR yields the best performance in improving groundwater predictions among the nine kernels for all case studies. The combined kernels MT_RQ_s, SE_RQ_s also perform well in groundwater predictions, and the commonly used SE kernel has mediocre performance in predicting groundwater observations. [ABSTRACT FROM AUTHOR]