Probabilistic numerical methods aim to model numerical error as a source of epistemic uncertainty that is subject to probabilistic analysis and reasoning, enabling the principled propagation of… (More)

There is renewed interest in formulating integration as a statistical inference problem, motivated by obtaining a full distribution over numerical error that can be propagated through subsequent… (More)

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 expectation of a… (More)

This paper studies the numerical computation of integrals, representing estimates or predictions, over the output f(x) of a computational model with respect to a distribution p(dx) over uncertain… (More)

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they… (More)

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… (More)

Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have… (More)

An important task in computational statistics and machine learning is to approximate a posterior distribution p(x) with an empirical measure supported on a set of representative points {xi}i=1. This… (More)