We describe the Bayesian analysis of nuclear dynamics (BAND) framework, a cyberinfrastructure that we are developing which will unify the treatment of nuclear models, experimental data, and associated uncertainties. We overview the statistical principles and nuclear-physics contexts underlying the BAND toolset, with an emphasis on Bayesian methodology’s ability to leverage insights from multiple models. In order to facilitate understanding of these tools, we provide a simple and accessible example of the BAND framework’s application. Four case studies are presented to highlight how elements of the framework will enable progress in complex, far-ranging problems in nuclear physics (NP). By collecting notation and terminology, providing illustrative examples, and giving an overview of the associated techniques, this paper aims to open paths through which the NP and statistics communities can contribute to and build upon the BAND framework.

Computer simulation has increasingly become popular for analysis of systems that cannot be feasibly changed because of costs or scale. This work proposes a method to construct an emulator for stochastic simulations by performing a designed experiment on the simulator and developing an emulative distribution. Existing emulators have focused on estimation of the mean of the simulation output, but this work presents an emulator for the distribution of the output. This construction provides both an explicit distribution and a fast sampling scheme. Beyond the emulator description, this work demonstrates the emulator's efficiency, that is, its convergence rate is the asymptotically optimal among all possible emulators using the same sample size (under certain conditions). An example of its practical use is demonstrated using a stochastic simulation of fracture mechanics. Supplementary materials for this article are available online.

Random field models have been widely employed to develop a predictor of an expensive function based on observations from an experiment. The traditional framework for developing a predictor with random field models can fail due to the computational burden it requires. This problem is often seen in cases where the input of the expensive function is high dimensional. While many previous works have focused on developing an approximative predictor to resolve these issues, this article investigates a different solution mechanism. We demonstrate that when a general set of designs is employed, the resulting predictor is quick to compute and has reasonable accuracy. The fast computation of the predictor is made possible through an algorithm proposed by this work. This paper also demonstrates methods to quickly evaluate the likelihood of the observations and describes some fast maximum likelihood estimates for unknown parameters of the random field. The computational savings can be several orders of magnitude when the input is located in a high dimensional space. Beyond the fast computation of the predictor, existing research has demonstrated that a subset of these designs generate predictors that are asymptotically efficient. This work details some empirical comparisons to the more common space-filling designs that verify the designs are competitive in terms of resulting prediction accuracy.

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multi-resolution functional ANOVA model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input non-linear regression problems.An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. New results on consistency and inference for the (potentially overlapping) group lasso in a high-dimensional setting are developed and applied to the proposed multi-resolution functional ANOVA model. Importantly, these results allow us to quantify the uncertainty in our predictions.Numerical examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, both in terms of sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy.

When producing engineered surfaces, the stochastic portion of the processing greatly affects the overall output quality. We propose a Gaussian process model that accounts for the impact of control variables on the stochastic elements of the produced surfaces. An optimization algorithm is outlined to find the maximum likelihood estimates of the model parameters. A case study involving the thickness surfaces of semiconductor wafers is examined that demonstrates the need for the proposed approach. Copyright © 2013 John Wiley & Sons Ltd