Fast Update of Conditional Simulation Ensembles

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• 作者：Clément Chevalier ; Xavier Emery ; David Ginsbourger
• 关键词：Gaussian random fields ; Residual kriging algorithm ; Batch ; sequential strategies ; Kriging update equations
• 刊名：Mathematical Geosciences
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：47
• 期：7
• 页码：771-789
• 全文大小：1,834 KB
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• 作者单位：Clément Chevalier (1)
  Xavier Emery (2)
  David Ginsbourger (3)
  
  1. Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057, Zurich, Switzerland
  2. Mining Engineering Department/Advanced Mining Technology Center, University of Chile, Avenida Tupper 2069, Santiago, Chile
  3. IMSV, Department of Mathematics and Statistics, University of Bern, Alpeneggstrasse 22, 3012, Bern, Switzerland
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Mathematical Applications in Geosciences
  Statistics for Engineering, Physics, Computer Science, Chemistry and Geosciences
  Geotechnical Engineering
  Hydrogeology
  
• 出版者：Springer Berlin Heidelberg
• ISSN：1874-8953

文摘

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