Calculating the expected information gain in optimal Bayesian experimental design typically relies on nested Monte Carlo sampling. When the model also contains nuisance parameters, which are parameters that contribute to the overall uncertainty of the system but are of no interest in the Bayesian design framework, this introduces a second inner loop. We propose and derive a small-noise approximation for this additional inner loop. The computational cost of our method can be further reduced by applying a Laplace approximation to the remaining inner loop. Thus, we present two methods, the small-noise Double-loop Monte Carlo and small-noise Monte Carlo Laplace methods. Moreover, we demonstrate that the total complexity of these two approaches remains comparable to the case without nuisance uncertainty. To assess the efficiency of these methods, we present three examples, and the last example includes the partial differential equation for the electrical impedance tomography experiment for composite laminate materials.
翻译:在最佳贝叶斯实验设计中,最佳贝叶斯实验设计的预期信息收益通常依赖于嵌套的蒙特卡洛取样。当模型还包含干扰参数时,这些参数有助于整个系统的整体不确定性,但对巴伊西亚设计框架没有兴趣,这就引入了第二个内环。我们为这一额外的内环提议并得出一个小噪音近似值。我们方法的计算成本可以通过对其余的内环应用拉普尔近比来进一步降低。因此,我们提出了两种方法,即小噪音双圈蒙特卡洛和小噪音蒙特卡洛拉帕特方法。此外,我们证明这两种方法的总复杂性仍然与案件相当,没有骚扰不确定性。为了评估这些方法的效率,我们举了三个例子,最后一个例子包括复合层状材料的阻碍电学实验部分差异方程。