Bayesian methods in engineering design problems.

This report discusses the applicability of Bayesian methods to engineering design problems. The attraction of Bayesian methods lies in their ability to integrate observed data and prior knowledge to form a posterior distribution estimate of a quantity of interest. Conceptually, Bayesian methods are desirable because they have the property of taking prior estimates and updating them with data over time. Bayesian statistics has been dominated by non-Bayesian approaches to inference for many years. However, over the past decade, there has been an emergence of Bayesian methods, driven by the availability of computational techniques. This report outlines Bayesian approaches which could be applied to engineering problems, particularly design optimization problems. This report first outlines the fundamental principles of Bayesian statistics. We discuss some simple applications of Bayesian inference, and then present more complex applications of Bayesian techniques applied to problems of calibration, optimization under uncertainty (OUU), and verification and validation (V&V). Specific applications of Bayesian methods to engineering problems include probability of failure estimation, Bayesian regression, Gaussian process models, and hierarchical or multi-fidelity models.