Proceedings of the International Conference on Structural Safety and Reliability, New York, NY.We quantify uncertainty in complex systems by a flexible, nonparametric framework for estimating probability density functions of output quantities of interest. The framework systematically incorporates
soft information about the system from engineering judgement and experience to improve the estimates and ensure that they are consistent with prior knowledge. The framework is based on a maximum likelihood criterion,
with epi-splines facilitating rapid solution of the resulting optimization problems. In four numerical examples
with few realizations of the system output, we identify the main features of output densities even for nonsmooth
and discontinuous system function and high-dimensional inputs
