Bayesian sensitivity analysis of a large nonlinear model

Within the discipline of uncertainty analysis in structural dynamics, a large open problem is concerned with the propagation of uncertainty through large nonlinear models (in the form of computer codes) when the expense of running the model makes Monte Carlo analysis prohibitively time-consuming. A sub-problem of concern here is the choice of which variables will make a significant contribution to the output uncertainty - this is the domain of sensitivity analysis. The object of the current paper is to apply a relatively new technique of Bayesian sensitivity analysis to the problem. In order to illustrate the methodology, a Finite Element (FE) model of the heart-valve system will be used. This is an example of some importance as the behaviour of the heart under physiological fluid-loading conditions will depend strongly on the properties of the tissue; however, these properties are not known with any accuracy and will in fact vary significantly from person to person.