no code implementations • 14 May 2024 • Marvin Pförtner, Jonathan Wenger, Jon Cockayne, Philipp Hennig

In this work, we propose a probabilistic numerical method for inference in high-dimensional Gauss-Markov models which mitigates these scaling issues.

no code implementations • 22 Apr 2021 • Junyang Wang, Jon Cockayne, Oksana Chkrebtii, T. J. Sullivan, Chris. J. Oates

The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied.

no code implementations • 1 Feb 2021 • Toni Karvonen, Jon Cockayne, Filip Tronarp, Simo Särkkä

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.

no code implementations • 23 Dec 2020 • Jon Cockayne, Ilse C. F. Ipsen, Chris J. Oates, Tim W. Reid

This paper presents a probabilistic perspective on iterative methods for approximating the solution $\mathbf{x}_* \in \mathbb{R}^d$ of a nonsingular linear system $\mathbf{A} \mathbf{x}_* = \mathbf{b}$.

no code implementations • 23 Dec 2020 • Jon Cockayne, Matthew M. Graham, Chris J. Oates, T. J. Sullivan

A learning procedure takes as input a dataset and performs inference for the parameters $\theta$ of a model that is assumed to have given rise to the dataset.

Bayesian Inference Statistics Theory Statistics Theory

no code implementations • 3 Sep 2020 • 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.

3 code implementations • pproximateinference AABI Symposium 2021 • Marina Riabiz, Wilson Chen, Jon Cockayne, Pawel Swietach, Steven A. Niederer, Lester Mackey, Chris. J. Oates

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.

3 code implementations • 16 Jan 2018 • Jon Cockayne, Chris Oates, Ilse Ipsen, Mark Girolami

The estimates obtained in this case are of little value unless further information can be provided about the numerical error.

Methodology Numerical Analysis Numerical Analysis Statistics Theory Statistics Theory

1 code implementation • 19 Jul 2017 • Chris. J. Oates, Jon Cockayne, Robert G. Aykroyd, Mark Girolami

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 ensure correct operation.

Applications

no code implementations • ICML 2017 • Francois-Xavier Briol, Chris. J. Oates, Jon Cockayne, Wilson Ye Chen, Mark Girolami

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 determined by the ratio $s/d$, where $s$ and $d$ encode the smoothness and dimension of the integrand.

no code implementations • 15 Jan 2017 • Jon Cockayne, Chris Oates, Tim Sullivan, Mark Girolami

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations.

Methodology Numerical Analysis Numerical Analysis Statistics Theory Statistics Theory

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