SIAM/ASA Journal on Uncertainty Quantification, Volume 9, Issue 2, Page 420-445, January 2021.
We study conjugate prior models in Bayesian spatial inversion. The spatial Kriging model may be phrased in a conjugate Bayesian inversion setting with a Gaussian prior model and a Gauss-linear likelihood function, resulting in a Gaussian posterior model. Spatial variables with unimodal, symmetric spatial histograms can be represented by this Kriging model. We generalize this Gaussian prior model by a selection mechanism, and this selection Gaussian prior model may represent multimodal, skewed, and/or peaked spatial variables. Also this selection Gaussian prior model is conjugate with respect to Gauss-linear likelihood functions. Hence the posterior model is selection Gaussian and analytically tractable. Efficient algorithms for simulation of and prediction in the selection Gaussian posterior model are defined. Model parameter inference in a maximum likelihood setting, which is simplified by the conjugate property, is also discussed. Moreover, we demonstrate that any conjugate prior model can be generalized by selection and still remain conjugate with respect to the actual likelihood function. Lastly, a seismic inversion case study is presented, and improvements of 20--40% in prediction mean-square-error, relative to traditional Gaussian inversion, are found.

中文翻译：

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贝叶斯空间反演和共轭选择高斯先验模型

SIAM / ASA不确定性量化期刊，第9卷，第2期，第420-445页，2021年1月。
我们研究贝叶斯空间反演中的共轭先验模型。可以在具有高斯先验模型和高斯线性似然函数的共轭贝叶斯反演设置中用短语表达空间Kriging模型，从而产生高斯后验模型。具有单峰，对称空间直方图的空间变量可以通过此Kriging模型表示。我们通过选择机制来概括该高斯先验模型，并且该选择高斯先验模型可以表示多峰，偏斜和/或峰值空间变量。同样，该选择高斯先验模型相对于高斯线性似然函数是共轭的。因此，后验模型是选择高斯模型并且在分析上易于处理。定义了用于选择高斯后验模型的仿真和预测的有效算法。还讨论了通过共轭特性简化的最大似然设置中的模型参数推断。此外，我们证明了任何共轭先验模型都可以通过选择进行概括，并且相对于实际似然函数仍然保持共轭。最后，提出了一个地震反演案例研究，与传统的高斯反演相比，预测均方误差提高了20--40％。