TY - JOUR
TI - Fast Update of Conditional Simulation Ensembles
UR - http://link.springer.com/article/10.1007/s11004-014-9573-7
KW - Gaussian random fields Residual kriging algorithm Batch-sequential strategies Kriging update equations
LA - en
AU - Chevalier, C.
AU - Emery, X.
AU - Ginsbourger, D.
PY - 2015
DA - .
AB - 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≥0 observations to an ensemble conditioned on n+q observations, for arbitrary q≥1. Compared to direct approaches, the proposed formulae prove to 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.
T2 - Mathematical Geosciences
IS - 7
VL - 47
SP - 771
EP - 789
ER -