We address the position of subjectivism within Bayesian statistics. We argue, first, that the subjectivist Bayes approach is the only feasible method for tackling many important practical problems. Second, we describe the essential role of the subjectivist approach in scientific analysis. Third, we consider possible modifications to the Bayesian approach from a subjectivist viewpoint. Finally, we address the issue of pragmatism in implementing the subjectivist approach.

Standard practice in analyzing data from different types of experiments is to treat data from each type separately. By borrowing strength across multiple sources, an integrated analysis can produce better results. Careful adjustments need to be made to incorporate the systematic differences among various experiments. To this end, some Bayesian hierarchical Gaussian process models (BHGP) are proposed. The heterogeneity among different sources is accounted for by performing flexible location and scale adjustments. The approach tends to produce prediction closer to that from the high-accuracy experiment. The Bayesian computations are aided by the use of Markov chain Monte Carlo and Sample Average Approximation algorithms. The proposed method is illustrated with two examples: one with detailed and approximate finite elements simulations for mechanical material design and the other with physical and computer experiments for modeling a food processor.

Abstract not found

In this work, we investigate the issue of providing a statistical model for the response of a computer model-described nuclear engineering system, for use in uncertainty propagation. The motivation behind our approach is the need for providing an uncertainty assessment even in the circumstances where only a few samples are available. Building on our recent work in using a regression approach with derivative information for approximating the system response, we investigate the ability of a universal gradientenhanced Kriging model to provide a means for inexpensive uncertainty quantification. The universal Kriging model can be viewed as a hybrid of polynomial regression and Gaussian process regression. For this model, the mean behavior of the surrogate is determined by a polynomial regression, and deviations from this mean are represented as a Gaussian process. Tests with explicit functions and nuclear engineering models show that the universal gradient-enhanced Kriging model provides a more accurate surrogate model when compared to either regression or ordinary Kriging models. In addition we investigate the ability of the Kriging model to provide error predictions and bounds for regression models.