Briol, FX; Oates, CJ; Girolami, M; Osborne, MA; Sejdinovic, D; (2019) Probabilistic integration: A role in statistical computation? Statistical Science , 34 (1) pp. 1-22. 10.1214/18-STS660.

Preview

Text Briol_Probabilistic integration. A role in statistical computation_VoR.pdf - Published Version Download (1MB) | Preview

Abstract

A research frontier has emerged in scientific computation, wherein discretisation error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical methods that enable the coherent propagation of probabilities through a (possibly deterministic) computational work-flow, in order to assess the impact of discretisation error on the computer output. This paper examines the case for probabilistic numerical methods in routine statistical computation. Our focus is on numerical integration, where a probabilistic integrator is equipped with a full distribution over its output that reflects the fact that the integrand has been discretised. Our main technical contribution is to establish, for the first time, rates of posterior contraction for one such method. Several substantial applications are provided for illustration and critical evaluation, including examples from statistical modelling, computer graphics and a computer model for an oil reservoir.

Download activity - last month

Export as CSVXMLJSON

Download activity - last 12 months

Export as JSONCSVXML

Downloads by country - last 12 months

Export as XMLCSVJSON

Archive Staff Only

View Item