140 citations · 1.9k across the 86 of their papers we have counts for
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Probabilistic Integration: A Role in Statistical Computation?
François-Xavier Briol, Chris. J. Oates, Mark Girolami +2
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statis…
Emulation of Higher-Order Tensors in Manifold Monte Carlo Methods for Bayesian Inverse Problems
Shiwei Lan, Tan Bui-Thanh, Mike Christie +1
The Bayesian approach to Inverse Problems relies predominantly on Markov Chain Monte Carlo methods for posterior inference. The typical nonlinear concentration of posterior measure…
Probability Measures for Numerical Solutions of Differential Equations
Patrick R. Conrad, Mark Girolami, Simo Särkkä +2
In this paper, we present a formal quantification of epistemic uncertainty induced by numerical solutions of ordinary and partial differential equation models. Numerical solutions…
Probabilistic Numerics and Uncertainty in Computations
Philipp Hennig, Michael A Osborne, Mark Girolami
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equation…
Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees
François-Xavier Briol, Chris J. Oates, Mark Girolami +1
There is renewed interest in formulating integration as an inference problem, motivated by obtaining a full distribution over numerical error that can be propagated through subsequ…
Unbiased Bayes for Big Data: Paths of Partial Posteriors
Heiko Strathmann, Dino Sejdinovic, Mark Girolami
A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consisten…