Markov chain Monte Carlo (MCMC) simulation methods are widely used to assess parametric uncertainties of hydrologic models conditioned on measurements of observable state variables. However, when the model is CPU‐intensive and high dimensional, the computational cost of MCMC simulation will be prohibitive. In this situation, a CPU‐efficient while less accurate low‐fidelity model (e.g., a numerical model with a coarser discretization or a data‐driven surrogate) is usually adopted. Nowadays, multifidelity simulation methods that can take advantage of both the efficiency of the low‐fidelity model and the accuracy of the high‐fidelity model are gaining popularity. In the MCMC simulation, as the posterior distribution of the unknown model parameters is the region of interest, it is wise to distribute most of the computational budget (i.e., the high‐fidelity model evaluations) therein. Based on this idea, in this paper we propose an adaptive multifidelity MCMC algorithm for efficient inverse modeling of hydrologic systems. In this method, we evaluate the high‐fidelity model mainly in the posterior region through iteratively running MCMC based on a Gaussian process system that is adaptively constructed with multifidelity simulation. The error of the Gaussian process system is rigorously considered in the MCMC simulation and gradually reduced to a negligible level in the posterior region. Thus, the proposed method can obtain an accurate estimate of the posterior distribution with a small number of the high‐fidelity model evaluations. The performance of the proposed method is demonstrated by three numerical case studies in inverse modeling of hydrologic systems.

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The ensemble Kalman filter (EnKF) has been widely used in parameter estimation for hydrological models. The focus of most previous studies was to develop more efficient analysis (estimation) algorithms. On the other hand, it is intuitively understandable that a well‐designed sampling (data‐collection) strategy should provide more informative measurements and subsequently improve the parameter estimation. In this work, a Sequential Ensemble‐based Optimal Design (SEOD) method, coupled with EnKF, information theory and sequential optimal design, is proposed to improve the performance of parameter estimation. Based on the first‐order and second‐order statistics, different information metrics including the Shannon entropy difference (SD), degrees of freedom for signal (DFS) and relative entropy (RE) are used to design the optimal sampling strategy, respectively. The effectiveness of the proposed method is illustrated by synthetic one‐dimensional and two‐dimensional unsaturated flow case studies. It is shown that the designed sampling strategies can provide more accurate parameter estimation and state prediction compared with conventional sampling strategies. Optimal sampling designs based on various information metrics perform similarly in our cases. The effect of ensemble size on the optimal design is also investigated. Overall, larger ensemble size improves the parameter estimation and convergence of optimal sampling strategy. Although the proposed method is applied to unsaturated flow problems in this study, it can be equally applied in any other hydrological problems.

The high mortality rate of lung squamous cell carcinoma (LUSC) is in part due to the lack of early detection of its biomarkers. The identification of key molecules involved in LUSC is therefore required to improve clinical diagnosis and treatment outcomes. The present study used the microarray datasets GSE31552, GSE6044 and GSE12428 from the Gene Expression Omnibus database to identify differentially expressed genes (DEGs). Kyoto Encyclopedia of Genes and Genomes (KEGG) and Gene Ontology (GO) enrichment analyses were conducted to construct the protein-protein interaction network of DEGs and hub genes module using STRING and Cytoscape. The 67 DEGs identified consisted of 42 upregulated genes and 25 downregulated genes. The pathways predicted by KEGG and GO enrichment analyses of DEGs mainly included cell cycle, cell proliferation, glycolysis or gluconeogenesis, and tetrahydrofolate metabolic process. Further analysis of the University of California Santa Cruz and ONCOMINE databases identified 17 hub genes. Overall, the present study demonstrated hub genes that were closely associated with clinical tissue samples of LUSC, and identified TYMS, CCNB2 and RFC4 as potential novel biomarkers of LUSC. The findings of the present study contribute to an improved understanding of the molecular mechanisms of carcinogenesis and progression of LUSC, and assist with the identification of potential diagnostic and therapeutic targets of LUSC.

Core Ideas The adaptive GP‐based MCMC was efficient to estimate hydraulic parameters in soils. Accuracy of the estimated parameters was verified by simulating experimental results. These simulations revealed a significant effect of layered structure on soil water flow. Modeling water movement in heterogeneous soils, e.g., layered soils, is an essential but challenging task that requires accurate estimation of multiple sets of soil hydraulic parameters. Markov chain Monte Carlo (MCMC) is a popular but computationally expensive method for parameter estimation. An adaptive Gaussian process (GP)‐based MCMC method proposed in our previous work presents significant computational efficiency. Nevertheless, its performance was evaluated only for synthetic numerical cases and has not been experimentally validated. Furthermore, its applicability in estimating hydraulic parameters of layered soils is still unknown. In this study, we systematically evaluated the performance of the GP‐based MCMC method in estimating the layered soil hydraulic parameters through a water infiltration experiment. It was shown that the proposed method could provide reliable estimations that were very close to those given by the original‐model‐based MCMC but at a much lower computational cost. The simulated soil water dynamics using the estimated parameters revealed a significant effect of layered heterogeneity on water flow. The lower layer(s) with higher water suction may cause persistent unsaturated status of the upper layer(s) during infiltration.