Groundwater contamination risk assessment for health-threatening compounds should benefit from a stochastic environmental risk assessment which considers the effects of biological, chemical, human behavioral, and physiological processes that involve elements of biotic and abiotic aquifer uncertainty, and human population variability. This paper couples a complex model of chemical degradation and transformation with movement in an aquifer undergoing bioremediation to generate a health risk analysis for different population cohorts in the community. A twostage Monte Carlo simulation has separate stages for population variability and aquifer uncertainty yielding a computationally efficient and conceptually attractive algorithm. A hypothetical example illustrates how risk variance analysis can be conducted to determine the distribution of risk, and the relative impact of uncertainty and variability in different sets of parameters upon the variation of risk values for adults, adolescents, and children. The groundwater example considers a community water supply contaminated with chlorinated ethenes. Biodegradation pathways are enhanced by addition of butyrate. The results showed that the contribution of uncertainty to the risk variance is comparable to that of variability. Among the uncertain parameters considered, transmissivity accounted for the major part of the output variance. Children were the most susceptible and vulnerable population cohort.

In the following article we consider approximate Bayesian computation (ABC) inference.We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation.Several numerical examples are given.

Abstract. Over the anthropocene methane has increased dramatically. Wetlands are one of the major sources of methane to the atmosphere, but the role of changes in wetland emissions is not well understood. The Community Land Model (CLM) of the Community Earth System Models contains a module to estimate methane emissions from natural wetlands and rice paddies. Our comparison of CH 4 emission observations at 16 sites around the planet reveals, however, that there are large discrepancies between the CLM predictions and the observations. The goal of our study is to adjust the model parameters in order to minimize the root mean squared error (RMSE) between model predictions and observations. These parameters have been selected based on a sensitivity analysis. Because of the cost associated with running the CLM simulation (15 to 30 min on the Yellowstone Supercomputing Facility), only relatively few simulations can be allowed in order to find a near-optimal solution within an acceptable time. Our results indicate that the parameter estimation problem has multiple local minima. Hence, we use a computationally efficient global optimization algorithm that uses a radial basis function (RBF) surrogate model to approximate the objective function. We use the information from the RBF to select parameter values that are most promising with respect to improving the objective function value. We show with pseudo data that our optimization algorithm is able to make excellent progress with respect to decreasing the RMSE. Using the true CH 4 emission observations for optimizing the parameters, we are able to significantly reduce the overall RMSE between observations and model predictions by about 50 %. The methane emission predictions of the CLM using the optimized parameters agree better with the observed methane emission data in northern and tropical latitudes. With the optimized parameters, the methane emission predictions are higher in northern latitudes than when the default parameters are used. For the tropics, the optimized parameters lead to lower emission predictions than the default parameters.

Automatically searching for optimal hyperparameter configurations is of crucial importance for applying deep learning algorithms in practice. Recently, Bayesian optimization has been proposed for optimizing hyperparameters of various machine learning algorithms. Those methods adopt probabilistic surrogate models like Gaussian processes to approximate and minimize the validation error function of hyperparameter values. However, probabilistic surrogates require accurate estimates of sufficient statistics (e.g., covariance) of the error distribution and thus need many function evaluations with a sizeable number of hyperparameters. This makes them inefficient for optimizing hyperparameters of deep learning algorithms, which are highly expensive to evaluate. In this work, we propose a new deterministic and efficient hyperparameter optimization method that employs radial basis functions as error surrogates. The proposed mixed integer algorithm, called HORD, searches the surrogate for the most promising hyperparameter values through dynamic coordinate search and requires many fewer function evaluations. HORD does well in low dimensions but it is exceptionally better in higher dimensions. Extensive evaluations on MNIST and CIFAR-10 for four deep neural networks demonstrate HORD significantly outperforms the well-established Bayesian optimization methods such as GP, SMAC, and TPE. For instance, on average, HORD is more than 6 times faster than GP-EI in obtaining the best configuration of 19 hyperparameters.

Abstract. Over the anthropocene methane has increased dramatically. Wetlands are one of the major sources of methane to the atmosphere, but the role of changes in wetland emissions is not well understood. The Community Land Model (CLM) of the Community Earth System Models contains a module to estimate methane emissions from natural wetlands and rice paddies. Our comparison of CH4 emission observations at 16 sites around the planet reveals, however, that there are large discrepancies between the CLM predictions and the observations. The goal of our study is to adjust the model parameters in order to minimize the root mean squared error (RMSE) between model predictions and observations. These parameters have been selected based on a sensitivity analysis. Because of the cost associated with running the CLM simulation (15 to 30 min on the Yellowstone Supercomputing Facility), only relatively few simulations can be allowed in order to find a near optimal solution within an acceptable time. Our results indicate that the parameter estimation problem has multiple local minima. Hence, we use a computationally efficient global optimization algorithm that uses a radial basis function (RBF) surrogate model to approximate the objective function. We use the information from the RBF to select parameter values that are most promising with respect to improving the objective function value. We show with pseudo data that our optimization algorithm is able to make excellent progress with respect to decreasing the RMSE. Using the true CH4 emission observations for optimizing the parameters, we are able to significantly reduce the overall RMSE between observations and model predictions by about 50%. The CLM predictions with the optimized parameters agree for northern and tropical latitudes more with the observed data than when using the default parameters and the emission predictions are higher than with default settings in northern latitudes and lower than default settings in the tropics.