87 citations · 196 across the 20 of their papers we have counts for
22 papers
SMRS: advocating a unified reporting standard for surrogate models in the artificial intelligence era
Elizaveta Semenova, Alisa Sheinkman, Timothy James Hitge +2
Surrogate models are widely used to approximate complex systems across science and engineering to reduce computational costs. Despite their widespread adoption, the field lacks sta…
Statistical Properties of the Probabilistic Numeric Linear Solver BayesCG
Tim W. Reid, Ilse C. F. Ipsen, Jon Cockayne +1
We analyse the calibration of BayesCG under the Krylov prior, a probabilistic numeric extension of the Conjugate Gradient (CG) method for solving systems of linear equations with s…
Theoretical Guarantees for the Statistical Finite Element Method
Yanni Papandreou, Jon Cockayne, Mark Girolami +1
The statistical finite element method (StatFEM) is an emerging probabilistic method that allows observations of a physical system to be synthesised with the numerical solution of a…
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…
A probabilistic Taylor expansion with Gaussian processes
Toni Karvonen, Jon Cockayne, Filip Tronarp +1
We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consist of deri…
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…
Testing whether a Learning Procedure is Calibrated
Jon Cockayne, Matthew M. Graham, Chris J. Oates +2
A learning procedure takes as input a dataset and performs inference for the parameters of a model that is assumed to have given rise to the dataset. Here we consider learning…
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…
BayesCG As An Uncertainty Aware Version of CG
Tim W. Reid, Ilse C. F. Ipsen, Jon Cockayne +1
The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of the Conjugate Gradient method (CG) for solving linear systems with real symmetric positive def…
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…
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…
Probabilistic Linear Solvers: A Unifying View
Simon Bartels, Jon Cockayne, Ilse C. F. Ipsen +1
Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, e…
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 in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment
Chris. J. Oates, Jon Cockayne, Robert G. Aykroyd +1
The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to e…
On the Sampling Problem for Kernel Quadrature
Francois-Xavier Briol, Chris J. Oates, Jon Cockayne +2
The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate d…
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…
Convergence Rates for a Class of Estimators Based on Stein's Method
Chris J. Oates, Jon Cockayne, François-Xavier Briol +1
Gradient information on the sampling distribution can be used to reduce the variance of Monte Carlo estimators via Stein's method. An important application is that of estimating an…