Iterative Bayesian inversion with Gaussian mixtures: finite sample implementation and large sample asymptotics

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• 作者：Andreas S. Stordal
• 关键词：Bayesian estimation ; Ensemble methods ; Gaussian mixtures ; Iterative importance sampling ; Data assimilation ; 62H ; 86
• 刊名：Computational Geosciences
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：19
• 期：1
• 页码：1-15
• 全文大小：1,084 KB
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• 作者单位：Andreas S. Stordal (1)
  
  1. IRIS, Bergen, Norway
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Modeling and IndustrialMathematics
  Geotechnical Engineering
  Hydrogeology
  Soil Science and Conservation
  
• 出版者：Springer Netherlands
• ISSN：1573-1499

文摘

Approximate solutions for Bayesian estimation in large scale models is a topic under investigation in many scientific communities. We define an iterative method based on the adaptive Gaussian mixture filter with batch updates as a robust alternative to adaptive importance sampling. We prove asymptotic optimality under certain conditions, contrary to other methods discussed where the sample distribution depends on the nonlinearity and scaling of the model. The finite sample implementation of the method is compared to an ensemble smoother with multiple data assimilation and an ensemble-based randomized maximum likelihood approach on a synthetic 1D reservoir model.