Citation

BibTex format

@article{Briol:10.1214/18-STS660,
author = {Briol, F-X and Oates, CJ and Girolami, M and Osborne, MA and Sejdinovic, D},
doi = {10.1214/18-STS660},
journal = {Statistical Science},
pages = {1--22},
title = {Probabilistic Integration: A Role in Statistical Computation?},
url = {http://dx.doi.org/10.1214/18-STS660},
volume = {34},
}

RIS format (EndNote, RefMan)

TY  - JOUR
AB - A research frontier has emerged in scientific computation, wherein numericalerror is regarded as a source of epistemic uncertainty that can be modelled.This raises several statistical challenges, including the design of statisticalmethods that enable the coherent propagation of probabilities through a(possibly deterministic) computational work-flow. This paper examines the casefor probabilistic numerical methods in routine statistical computation. Ourfocus is on numerical integration, where a probabilistic integrator is equippedwith a full distribution over its output that reflects the presence of anunknown numerical error. Our main technical contribution is to establish, forthe first time, rates of posterior contraction for these methods. These showthat probabilistic integrators can in principle enjoy the "best of bothworlds", leveraging the sampling efficiency of Monte Carlo methods whilstproviding a principled route to assess the impact of numerical error onscientific conclusions. Several substantial applications are provided forillustration and critical evaluation, including examples from statisticalmodelling, computer graphics and a computer model for an oil reservoir.
AU - Briol,F-X
AU - Oates,CJ
AU - Girolami,M
AU - Osborne,MA
AU - Sejdinovic,D
DO - 10.1214/18-STS660
EP - 22
SN - 0883-4237
SP - 1
TI - Probabilistic Integration: A Role in Statistical Computation?
T2 - Statistical Science
UR - http://dx.doi.org/10.1214/18-STS660
UR - http://arxiv.org/abs/1512.00933v6
UR - http://hdl.handle.net/10044/1/67126
VL - 34
ER -