Sequential Design of Computer Experiments for the Solution of Bayesian Inverse Problems
Sequential Design of Computer Experiments for the Solution of Bayesian Inverse Problems
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DOI：
10.1137/15m1047659
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发表时间：
2017-07
期刊：
影响因子：
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通讯作者：
Michael Sinsbeck;W. Nowak
中科院分区：
文献类型：
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作者：
Michael Sinsbeck;W. Nowak
我们提出了一个序贯设计策略，在贝叶斯反问题的解决方案中的模型函数的有效采样。模型函数被假设为计算上昂贵的，因此由随机场（诸如高斯过程仿真器）描述。序贯设计策略是一种贪婪的一步向前看的方法，最小化贝叶斯风险相对于损失函数测量的平方L^2 $-误差的似然估计。四个数值例子表明，所提出的抽样方法是更有效的空间填充，基于先验的设计。
We present a sequential design strategy for efficient sampling of model functions during the solution of Bayesian inverse problems. The model function is assumed to be computationally expensive and therefore is described by a random field (such as a Gaussian process emulator). The sequential design strategy is a greedy one-step look ahead method, minimizing the Bayes risk with respect to a loss function measuring the quadratic $L^2$-error in the likelihood estimate. Four numerical examples demonstrate that the proposed sampling method is more efficient than space-filling, prior-based designs.