3 citations · 3 across the 1 of their papers we have counts for
6 papers
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…
Probabilistic Iterative Methods for Linear Systems
Jon Cockayne, Ilse C. F. Ipsen, Chris J. Oates +1
This paper presents a probabilistic perspective on iterative methods for approximating the solution of a nonsingular linear system $\mathbf{A} \math…
Probabilistic Gradients for Fast Calibration of Differential Equation Models
Jon Cockayne, Andrew B. Duncan
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottl…
A Role for Symmetry in the Bayesian Solution of Differential Equations
Junyang Wang, Jon Cockayne, Chris J. Oates
The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators suggests that formal uncertainty quantification can also…
Optimality Criteria for Probabilistic Numerical Methods
Chris. J. Oates, Jon Cockayne, Dennis Prangle +2
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for…
On the Bayesian Solution of Differential Equations
Junyang Wang, Jon Cockayne, Chris Oates
The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators allows for formal statistical quantification of the error…