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首页> 外文期刊>ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B. Mechanical Engineering >Optimal Experimental Design Using a Consistent Bayesian Approach
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Optimal Experimental Design Using a Consistent Bayesian Approach

机译：使用一致的贝叶斯方法最佳实验设计

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摘要

We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent Bayesian approach for solving stochastic inverse problems, which seeks a posterior probability density that is consistent with the model and the data in the sense that the push-forward of the posterior (through the computational model) matches the observed density on the observations almost everywhere. Given a set of potential observations, our optimal experimental design (OED) seeks the observation, or set of observations, that maximizes the expected information gain from the prior probability density on the model parameters. We discuss the characterization of the space of observed densities and a computationally efficient approach for rescaling observed densities to satisfy the fundamental assumptions of the consistent Bayesian approach. Numerical results are presented to compare our approach with existing OED methodologies using the classical/statistical Bayesian approach and to demonstrate our OED on a set of representative partial differential equations (PDE)-based models.
机译：我们考虑利用计算模型来指导最佳采集实验数据，以通知模型输入参数的随机描述。我们的配方基于最近开发的一致的贝叶斯人方法，用于解决随机逆问题，该方法寻求与模型和数据相一致的后验概率密度，以至于后部的推进（通过计算模型）几乎无处不在地匹配观察到的观察密度。鉴于一组潜在的观察，我们的最佳实验设计（OED）寻求观察或一组观察，从而最大化了模型参数上的先前概率密度的预期信息增益。我们讨论了观察到的密度空间的表征和用于重新定义的密度的计算有效的方法，以满足一致的贝叶斯方法的根本假设。提出了使用经典/统计贝叶斯方法的现有OED方法的方法，并在一组代表性部分微分方程（PDE）的模型上展示我们对现有OED方法的方法。

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