Publications (4)
Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)
Ege Ozsar, Misha Kilmer, Eric Miller +2
We introduce PaLEnTIR, a significantly enhanced parametric level-set (PaLS) method addressing the restoration and reconstruction of piecewise constant objects. Our key contribution…
Monte Carlo Methods for Estimating the Diagonal of a Real Symmetric Matrix
Eric Hallman, Ilse C. F. Ipsen, Arvind Saibaba
For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds…
Low Rank Independence Samplers in Bayesian Inverse Problems
D. Andrew Brown, Arvind Saibaba, Sarah Vallélian
In Bayesian inverse problems, the posterior distribution is used to quantify uncertainty about the reconstructed solution. In practice, Markov chain Monte Carlo algorithms often ar…
Hyper-differential sensitivity analysis in the context of Bayesian inference applied to ice-sheet problems
William Reese, Joseph Hart, Bart van Bloemen Waanders +3
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain…