663 citations · 1.3k across the 32 of their papers we have counts for
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math.PR2017★ 17 cited
Uncertainty quantification for complex systems with very high dimensional response using Grassmann manifold variations
D. G Giovanis, M. D. Shields
This paper addresses uncertainty quantification (UQ) for problems where scalar (or low-dimensional vector) response quantities are insufficient and, instead, full-field (very high-…
stat.CO2017★ 42 cited
The effect of prior probabilities on quantification and propagation of imprecise probabilities resulting from small datasets
Jiaxin Zhang, Michael D. Shields
This paper outlines a methodology for Bayesian multimodel uncertainty quantification (UQ) and propagation and presents an investigation into the effect of prior probabilities on th…
math.NA2017★ 29 cited
Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis
Anindya Bhaduri, Yanyan He, Michael D. Shields +2
Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in…