Probabilistic Integration: A Role in Statistical Computation?
Probabilistic Integration: A Role in Statistical Computation?
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DOI：
10.1214/18-sts660
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发表时间：
2019-02-01
影响因子：
5.7
通讯作者：
Sejdinovic, Dino
中科院分区：
文献类型：
--
作者：
Briol, Francois-Xavier;Oates, Chris J.;Sejdinovic, Dino
科学计算领域出现了一个研究前沿，其中离散误差被视为可以建模的认知不确定性的来源。这提出了一些统计挑战，包括设计统计方法，通过（可能是确定性的）计算工作流程实现概率的相干传播，以评估离散误差对计算机输出的影响。本文研究了常规统计计算中概率数值方法的情况。我们的重点是数值积分，其中概率积分器配备了其输出的完整分布，反映了被积函数已离散化的事实。我们的主要技术贡献是首次确定此类方法的后收缩率。提供了几个重要的应用程序用于说明和关键评估，包括统计建模、计算机图形学和油藏计算机模型的示例。
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.