Fast Update of Conditional Simulation Ensembles
Chevalier, Clément ; Emery, Xavier ; Ginsbourger, David
In: Mathematical Geosciences, 2015, vol. 47, no. 7, p. 771-789
Ajouter à la liste personnelle- Summary
- 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 minimal cost. Explicit formulae are provided, which allow updating an ensemble of sample paths conditioned on $$n\ge 0$$ n ≥ 0 observations to an ensemble conditioned on $$n+q$$ n + q observations, for arbitrary $$q\ge 1$$ q ≥ 1 . Compared to direct approaches, the proposed formulae prove to substantially reduce computational complexity. Moreover, these formulae explicitly exhibit how the $$q$$ 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.