Probabilistic integration: A role in statistical computation?
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...
| मुख्य लेखकों: | , , , , |
|---|---|
| स्वरूप: | Journal article |
| प्रकाशित: |
Institute of Mathematical Statistics
2019
|
| _version_ | 1826293167131983872 |
|---|---|
| author | Briol, F Oates, C Girolami, M Osborne, M Sejdinovic, D |
| author_facet | Briol, F Oates, C Girolami, M Osborne, M Sejdinovic, D |
| author_sort | Briol, F |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T03:25:55Z |
| format | Journal article |
| id | oxford-uuid:b9074917-fecb-41a6-a2eb-62fe47ae715f |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:25:55Z |
| publishDate | 2019 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:b9074917-fecb-41a6-a2eb-62fe47ae715f2022-03-27T05:00:14ZProbabilistic integration: A role in statistical computation?Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b9074917-fecb-41a6-a2eb-62fe47ae715fSymplectic Elements at OxfordInstitute of Mathematical Statistics2019Briol, FOates, CGirolami, MOsborne, MSejdinovic, DA 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. |
| spellingShingle | Briol, F Oates, C Girolami, M Osborne, M Sejdinovic, D Probabilistic integration: A role in statistical computation? |
| title | Probabilistic integration: A role in statistical computation? |
| title_full | Probabilistic integration: A role in statistical computation? |
| title_fullStr | Probabilistic integration: A role in statistical computation? |
| title_full_unstemmed | Probabilistic integration: A role in statistical computation? |
| title_short | Probabilistic integration: A role in statistical computation? |
| title_sort | probabilistic integration a role in statistical computation |
| work_keys_str_mv | AT briolf probabilisticintegrationaroleinstatisticalcomputation AT oatesc probabilisticintegrationaroleinstatisticalcomputation AT girolamim probabilisticintegrationaroleinstatisticalcomputation AT osbornem probabilisticintegrationaroleinstatisticalcomputation AT sejdinovicd probabilisticintegrationaroleinstatisticalcomputation |