Mathematical Geosciences

, Volume 47, Issue 7, pp 771–789 | Cite as

Fast Update of Conditional Simulation Ensembles

  • Clément Chevalier
  • Xavier Emery
  • David Ginsbourger
Article

Abstract

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 \(n\ge 0\) observations to an ensemble conditioned on \(n+q\) observations, for arbitrary \(q\ge 1\). 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.

Keywords

Gaussian random fields Residual kriging algorithm   Batch-sequential strategies Kriging update equations 

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Copyright information

© International Association for Mathematical Geosciences 2014

Authors and Affiliations

  • Clément Chevalier
    • 1
  • Xavier Emery
    • 2
  • David Ginsbourger
    • 3
  1. 1.Institute of MathematicsUniversity of ZurichZurichSwitzerland
  2. 2.Mining Engineering Department/Advanced Mining Technology CenterUniversity of ChileSantiagoChile
  3. 3.IMSV, Department of Mathematics and StatisticsUniversity of BernBernSwitzerland

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