The weighting of critical-point samples in the weighted randomized maximum likelihood method depend on the magnitude of the data mismatch at the critical points and on the Jacobian of the transformation from the prior density to the proposal density. When standard iterative ensemble smoothers are applied for data assimilation, the Jacobian is identical for all samples. If a hybrid data assimilation method is applied, however, there is the possibility that each ensemble member can have a distinct Jacobian and that the posterior density can be multimodal. In order to apply a hybrid method iterative ensemble smoother, it is necessary that a part of the transformation from the prior Gaussian random variable to the data be analytic. Examples might include analytic transformation from a latent Gaussian random variable to permeability followed by a black-box transformation from permeability to state variables in porous media flow, or a Gaussian hierarchical model for variables followed by a similar black-box transformation from permeability to state variables. In this paper, we investigate the application of weighting to both types of examples.
翻译:加权随机最大可能性方法中关键点样本的加权权重取决于临界点数据错配的程度,取决于从先前密度向建议密度变异的雅各基体。当数据同化应用标准迭代共性平滑器时,所有样本的雅各基点均相同。但如果采用混合数据同化方法,每个共性成员都有可能有一个不同的雅各克,后端密度可以是多式联运。为了应用混合方法迭代共性平滑,必须使先前高斯随机变量向数据转换的一部分具有分析性。举例可能包括从潜高斯随机变异到渗透性的分析性变异,随后是黑盒变异,从易感变到多孔媒体流中的状态变变异,或高斯级变异模型,随后是类似黑盒变异的变异,从易感变异性到状态变异性。在本文中,我们调查对两种例子的加权应用情况。