132 citations · 604 across the 33 of their papers we have counts for
9 papers · 1 filter
Bayesian Numerical Methods for Nonlinear Partial Differential Equations
Junyang Wang, Jon Cockayne, Oksana Chkrebtii +2
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differe…
Randomised one-step time integration methods for deterministic operator differential equations
Han Cheng Lie, Martin Stahn, T. J. Sullivan
Uncertainty quantification plays an important role in problems that involve inferring a parameter of an initial value problem from observations of the solution. Conrad et al.\ (\te…
Optimal Bounds on Nonlinear Partial Differential Equations in Model Certification, Validation, and Experimental Design
M. McKerns, F. J. Alexander, K. S. Hickmann +2
We demonstrate that the recently developed Optimal Uncertainty Quantification (OUQ) theory, combined with recent software enabling fast global solutions of constrained non-convex o…
Adaptive reconstruction of imperfectly-observed monotone functions, with applications to uncertainty quantification
L. Bonnet, J. -L. Akian, É. Savin +1
Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive…
Comments on the article "A Bayesian conjugate gradient method"
T. J. Sullivan
The recent article "A Bayesian conjugate gradient method" by Cockayne, Oates, Ipsen, and Girolami proposes an approximately Bayesian iterative procedure for the solution of a syste…
A Modern Retrospective on Probabilistic Numerics
C. J. Oates, T. J. Sullivan
This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual dev…