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<p>I consider Bayesian model weighting (BMW), which is an essential component in realistic uncertainty quantification. The main motivation is field-scale porous-media-flow problems, where existing methods such as Bayesian model averaging (BMA), Bayesian stacking (BS), and Modified Bayesian stacking (MBS), typically are computationally infeasible. The main computational obstacle with BMA and MBS is use of Monte-Carlo (MC) integration where the integrand involves a data misfit in high dimensions, suffering from the curse of dimensionality. I propose a novel class of methods for BMW that in essence replaces a single high-dimensional MC integration with a modest number of MC integrations not suffering from the curse of dimensionality. The novel class of methods can be utilized both within the BMA and MBS frameworks. The computational gain with respect to plain BMA and MBS is quantified, and three methods from the novel class are applied to three examples. The first example is a modified version of Model 1 in the Society of Petroleum Engineers Comparative Solution Project, while the two other examples utilize data, simulation results, and additional information from the G-segment of the Norne field in the North Sea.</p>

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Bayesian model-feature weighting

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月29日

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  • Trond Mannseth

摘要

I consider Bayesian model weighting (BMW), which is an essential component in realistic uncertainty quantification. The main motivation is field-scale porous-media-flow problems, where existing methods such as Bayesian model averaging (BMA), Bayesian stacking (BS), and Modified Bayesian stacking (MBS), typically are computationally infeasible. The main computational obstacle with BMA and MBS is use of Monte-Carlo (MC) integration where the integrand involves a data misfit in high dimensions, suffering from the curse of dimensionality. I propose a novel class of methods for BMW that in essence replaces a single high-dimensional MC integration with a modest number of MC integrations not suffering from the curse of dimensionality. The novel class of methods can be utilized both within the BMA and MBS frameworks. The computational gain with respect to plain BMA and MBS is quantified, and three methods from the novel class are applied to three examples. The first example is a modified version of Model 1 in the Society of Petroleum Engineers Comparative Solution Project, while the two other examples utilize data, simulation results, and additional information from the G-segment of the Norne field in the North Sea.