Fast Update of Conditional Simulation Ensembles

Chevalier, Clément; Emery, Xavier; Ginsbourger, David (2015). Fast Update of Conditional Simulation Ensembles. Mathematical Geosciences, 47(7), pp. 771-789. Springer 10.1007/s11004-014-9573-7

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Gaussian random field (GRF) conditional simulation is a key ingredient in many spatial statistics problems for computing Monte-Carlo estimators and quantifying uncertainties on non-linear functionals of GRFs conditional on data. Conditional simulations are known to often be computer intensive, especially when appealing to matrix decomposition approaches with a large number of simulation points. This work studies settings where conditioning observations are assimilated batch sequentially, with one point or a batch of points at each stage. Assuming that conditional simulations have been performed at a previous stage, the goal is to take advantage of already available sample paths and by-products to produce updated conditional simulations at mini- mal cost. Explicit formulae are provided, which allow updating an ensemble of sample paths conditioned on n ≥ 0 observations to an ensemble conditioned on n + q observations, for arbitrary q ≥ 1. Compared to direct approaches, the proposed formulae proveto substantially reduce computational complexity. Moreover, these formulae explicitly exhibit how the q new observations are updating the old sample paths. Detailed complexity calculations highlighting the benefits of this approach with respect to state-of-the-art algorithms are provided and are complemented by numerical experiments.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Ginsbourger, David

Subjects:

500 Science > 510 Mathematics
500 Science > 550 Earth sciences & geology

ISSN:

1874-8961

Publisher:

Springer

Projects:

[UNSPECIFIED] ReDICE
[UNSPECIFIED] ENSEMBLE

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

10 Sep 2015 14:49

Last Modified:

13 Dec 2015 02:30

Publisher DOI:

10.1007/s11004-014-9573-7

BORIS DOI:

10.7892/boris.71474

URI:

https://boris.unibe.ch/id/eprint/71474

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