Simulation-Based Optimal Design Using a Response Variance Criterion
Simulation-Based Optimal Design Using a Response Variance Criterion
复制标题
使用响应方差准则的基于仿真的优化设计
DOI：
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发表时间：
2012
期刊：
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通讯作者：
M. Laine
中科院分区：
文献类型：
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作者：
A. Solonen;H. Haario;M. Laine
经典的优化设计准则在应用于非线性问题时存在两大缺陷。首先，它们基于围绕未知参数的点估计对模型进行线性化，因此依赖于该参数的不确定值。其次，经典的设计方法在不适定的估计情况下是不可用的，因为以前的数据缺乏正确构建设计标准所需的信息。贝叶斯优化设计原则上可以解决这些问题。然而，贝叶斯设计方法没有得到广泛应用，主要是因为没有有效和健壮的日常使用的标准实现。在本文中，我们根据Muller，Sanso和De Iorio(2004)提出的基于模拟的设计概念，指出了实现贝叶斯最优设计的具体方法。我们进一步发展了一种预测方差准则，并引入了一种有效计算方差的重要性加权机制。这种基于模拟的方法允许人们在参数估计过程的早期阶段，在经典设计标准不可用的情况下，开始基于模型的实验优化。我们证明，该方法可以显著减少在参数估计中获得所需精度所需的实验数量。在一个简单的案例中实施该方法的计算机代码包作为补充材料提供(可在网上获得)。
Classical optimal design criteria suffer from two major flaws when applied to nonlinear problems. First, they are based on linearizing the model around a point estimate of the unknown parameter and therefore depend on the uncertain value of that parameter. Second, classical design methods are unavailable in ill-posed estimation situations, where previous data lack the information needed to properly construct the design criteria. Bayesian optimal design can, in principle, solve these problems. However, Bayesian design methods are not widely applied, mainly due to the fact that standard implementations for efficient and robust routine use are not available. In this article, we point out a concrete recipe for implementing Bayesian optimal design, based on the concept of simulation-based design introduced by Muller, Sanso, and De Iorio (2004). We develop further a predictive variance criterion and introduce an importance weighting mechanism for efficient computation of the variances. The simulation-based approach allows one to start the model-based optimization of experiments at an early stage of the parameter estimation process, in situations where the classical design criteria are not available. We demonstrate that the approach can significantly reduce the number of experiments needed to obtain a desired level of accuracy in the parameter estimates. A computer code package that implements the approach in a simple case is provided as supplemental material (available online).