Abstract The common classical approach for finding optimal design is minimizing the variance of an unbiased maximum likelihood estimator (MLE) of parameters. However, under regularity condition, the variance of MLE is approximated by the Cramer–Rao lower bound. In this article, optimal designs are obtained under non-regularity condition in non-linear models. In the Bayesian approach, conditional mutual information is used to propose a new optimality criterion; Bayesian optimal design maximizes the mutual information between the observation and the model parameters. A Bayesian compound criterion is also provided to facilitate the performance comparison of the optimal designs. Finally, the equivalence theorem is given for criterion to allow for checking the optimality of the obtained Bayesian design points.

中文翻译：

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非正则条件下非线性模型的贝叶斯优化设计

摘要 寻找最优设计的常见经典方法是最小化参数的无偏最大似然估计量 (MLE) 的方差。然而，在正则条件下，MLE 的方差由 Cramer-Rao 下界近似。在本文中，在非线性模型的非正则条件下获得了最优设计。在贝叶斯方法中，使用条件互信息来提出新的最优性准则；贝叶斯优化设计最大化了观测与模型参数之间的互信息。还提供了贝叶斯复合标准，以促进最佳设计的性能比较。最后，给出了等价定理作为准则，以允许检查所获得的贝叶斯设计点的最优性。