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Activity Number: 351
Type: Topic Contributed
Date/Time: Tuesday, August 2, 2016 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #318845 View Presentation
Title: Probabilistic Integration: A Role for Statisticians in Numerical Analysis?
Author(s): Francois-Xavier Briol* and Chris J. Oates and Mark Girolami and Michael A. Osborne and Dino Sejdinovic
Companies: University of Warwick and University of Technology Sydney and University of Warwick/The Alan Turing Institute for Data Science and University of Oxford and University of Oxford
Keywords: Probabilistic numerics ; Numerical integration ; Markov chain Monte Carlo ; Quasi-Monte Carlo ; Bayesian nonparametrics ; Kernel methods

A research frontier has emerged in scientific computation, founded on the principle that numerical error entails epistemic uncertainty that ought to be subjected to statistical analysis. This viewpoint raises several interesting challenges, including the design of statistical methods that enable the coherent propagation of probabilities through a (possibly deterministic) computational pipeline. This paper examines the case for probabilistic numerical methods in statistical computation and a specific case study is presented for Markov chain and Quasi Monte Carlo methods. A probabilistic integrator is equipped with a full distribution over its output, providing a measure of epistemic uncertainty that is shown to be statistically valid at finite computational levels, as well as in asymptotic regimes. The approach is motivated by expensive integration problems, where, as in krigging, one is willing to expend cubic computational effort in order to gain uncertainty quantification. There, probabilistic integrators enjoy the "best of both worlds", leveraging the sampling efficiency of Monte Carlo methods whilst providing a principled route to assessment of the impact of numerical

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