87 citations · 196 across the 20 of their papers we have counts for
9 papers · 1 filter
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…
Optimal Thinning of MCMC Output
Marina Riabiz, Wilson Chen, Jon Cockayne +4
The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. T…
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…
A Bayesian Conjugate Gradient Method
Jon Cockayne, Chris Oates, Ilse Ipsen +1
A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solu…
Bayesian Probabilistic Numerical Methods
Jon Cockayne, Chris Oates, Tim Sullivan +1
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be…
Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems
Jon Cockayne, Chris Oates, Tim Sullivan +1
This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables th…
Comments on "Bayesian Solution Uncertainty Quantification for Differential Equations" by Chkrebtii, Campbell, Calderhead & Girolami
Jon Cockayne
I would like to thank the authors for their interesting and very clearly presented paper discussing probabilistic solvers for ODEs and PDEs.
Probabilistic Numerical Methods for Partial Differential Equations and Bayesian Inverse Problems
Jon Cockayne, Chris Oates, Tim Sullivan +1
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problem…