87 citations · 415 across the 70 of their papers we have counts for
6 papers · 1 filter
Posterior Integration on a Riemannian Manifold
Chris. J. Oates, Alessandro Barp, Mark Girolami
The geodesic Markov chain Monte Carlo method and its variants enable computation of integrals with respect to a posterior supported on a manifold. However, for regular integrals, t…
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…
Optimal Monte Carlo integration on closed manifolds
Martin Ehler, Manuel Graef, Chris. J. Oates
The worst case integration error in reproducing kernel Hilbert spaces of standard Monte Carlo methods with n random points decays as . However, re-weighting of random poi…
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…