A Consistent Bayesian Formulation for Stochastic Inverse Problems Based on Push-forward Measures
A Consistent Bayesian Formulation for Stochastic Inverse Problems Based on Push-forward Measures
复制标题
基于前推测度的随机反问题的一致贝叶斯公式
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
T. Wildey
中科院分区：
文献类型：
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作者：
T. Butler;J. Jakeman;T. Wildey
我们制定，并提出了一个数值方法来解决，从随机观测数据（感兴趣的数量）推断确定性模型的参数的反问题。该解决方案，作为一个概率测度，是使用贝叶斯更新方法的可测量的地图，找到一个后验概率测度，当通过确定性模型传播时，产生一个向前推的措施，完全匹配的数据上观察到的概率测度。我们的方法来寻找这样的后验措施，我们称之为一致的贝叶斯推理，是简单的，只需要计算的前推概率测度的先验概率测度和确定性模型的组合引起的。我们建立了观测一致后验的存在性和唯一性，并给出了稳定性和误差分析。我们还讨论了一致的贝叶斯推理，经典/统计贝叶斯推理，和最近开发的测量理论的推理方法之间的关系。最后，分析和数值结果突出的一致贝叶斯方法的某些属性和这种方法之间的差异和上述两种替代推理。
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is derived using a Bayesian updating approach for measurable maps that finds a posterior probability measure, that when propagated through the deterministic model produces a push-forward measure that exactly matches the observed probability measure on the data. Our approach for finding such posterior measures, which we call consistent Bayesian inference, is simple and only requires the computation of the push-forward probability measure induced by the combination of a prior probability measure and the deterministic model. We establish existence and uniqueness of observation-consistent posteriors and present stability and error analysis. We also discuss the relationships between consistent Bayesian inference, classical/statistical Bayesian inference, and a recently developed measure-theoretic approach for inference. Finally, analytical and numerical results are presented to highlight certain properties of the consistent Bayesian approach and the differences between this approach and the two aforementioned alternatives for inference.