Probabilistic Numerics

British Library, 19th-20th November 2015

Main organisers: Mark Girolami, Andrew Stuart, Ben Leimkuhler, Arthur Gretton, Zoubin Ghahramani, Mike Osborne

The emergence of Data Science as a discipline synthesising mathematics, statistical science, and computer science has brought enormous opportunities of intellectual and commercial benefit that neither field on its own could provide. With these many opportunities comes major research challenges at both the foundational and translational ends of the spectrum. The urgent and unmet need to formally analyse, design, develop and deploy advanced methods and algorithms that can scale in statistical and computational efficiency to the size of modern day data and complexity of mathematical models must be addressed.

The nexus of improving statistical quantification of uncertainty, more statistically and computationally efficient estimation of quantities of importance, more scalable and effective numerical methods, the compact and efficient programming representation of statistical models is represented in the emerging research theme of Probabilistic Numerics (PN).

It has long been known that there is a conceptual similarity between computation in numerical mathematics and inference in statistics. That is, numerical algorithms estimate latent quantities from incomplete information, collected by performing tractable computations. While this observation was long seen as primarily of philosophical value, recent results have highlighted its practical potential and now provide stricter mathematical connections between certain numerical methods and statistical estimation. Because numerical methods are the backbone of scientific computing, PN has a multitude of applications across a broad range of scientific and industrial areas. They can help reduce crippling computational costs by allowing computations to stop early, avoid redundant computations by propagating information between related computations, and incorporate salient prior information to speed up important classes of computations.