5 citations · 16 across the 13 of their papers we have counts for
8 papers · 1 filter
A Primer on the Karhunen-Loève Expansion
Alen Alexanderian
This article provides a primer on the spectral representation of random fields via the Karhunen-Loève Expansion (KLE). The goal is to bridge the gap between the theoretical foundat…
Robust optimal design of large-scale Bayesian nonlinear inverse problems
Abhijit Chowdhary, Ahmed Attia, Alen Alexanderian
We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maxim…
Sensitivity Analysis of the Information Gain in Infinite-Dimensional Bayesian Linear Inverse Problems
Abhijit Chowdhary, Shanyin Tong, Georg Stadler +1
We study the sensitivity of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs) with respect to modeling uncertainties. In parti…
Hyper-differential sensitivity analysis for nonlinear Bayesian inverse problems
Isaac Sunseri, Alen Alexanderian, Joseph Hart +1
We consider hyper-differential sensitivity analysis (HDSA) of nonlinear Bayesian inverse problems governed by PDEs with infinite-dimensional parameters. In previous works, HDSA has…
Global sensitivity analysis of rare event probabilities
Michael Merritt, Alen Alexanderian, Pierre Gremaud
By their very nature, rare event probabilities are expensive to compute; they are also delicate to estimate as their value strongly depends on distributional assumptions on the mod…
Monte Carlo Estimators for the Schatten p-norm of Symmetric Positive Semidefinite Matrices
Ethan Dudley, Arvind K. Saibaba, Alen Alexanderian
We present numerical methods for computing the Schatten -norm of positive semi-definite matrices. Our motivation stems from uncertainty quantification and optimal experimental d…