# Fast Update of Conditional Simulation Ensembles

3 Department of Mining Engineering and Advanced Mining Technology Center
Department of Mining Engineering and Advanced Mining Technology Center
Abstract : Gaussian random fields (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. Here we study the settings where conditioning observations are assimilated batch-sequentially, i.e. one point or batch of points at each stage. Assuming that conditional simulations have been performed at a previous stage, we aim at taking advantage of already available sample paths and by-products in order to produce updated conditional simulations at minimal cost. We provide explicit formulas allowing to update an ensemble of sample paths conditioned on $n\geq 0$ observations to an ensemble conditioned on $n+q$ observations, for arbitrary $q\geq 1$. Compared to direct approaches, the proposed formulas prove to substantially reduce computational complexity. Moreover, these formulas enable explicitly exhibiting how the $q$ ''new'' observations are updating the ''old'' sample paths. Detailed complexity calculations highlighting the benefits of our approach with respect to state-of-the-art algorithms are provided and are complemented by numerical experiments.
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Cited literature [20 references]

https://hal.archives-ouvertes.fr/hal-00984515
Contributor : David Ginsbourger <>
Submitted on : Monday, April 28, 2014 - 2:58:39 PM
Last modification on : Wednesday, May 6, 2020 - 8:18:02 PM
Long-term archiving on: : Monday, July 28, 2014 - 11:45:41 AM

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• HAL Id : hal-00984515, version 1

### Citation

Clément Chevalier, Xavier Emery, David Ginsbourger. Fast Update of Conditional Simulation Ensembles. 2014. ⟨hal-00984515⟩

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