Calculating the expected information gain in optimal Bayesian experimental design typically relies on nested Monte Carlo sampling. When the model also contains nuisance parameters, 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计算预期获得的信息通常依赖于嵌套的蒙特卡洛取样。 当模型还包含骚扰性参数时, 此模型引入了第二个内环。 我们为这个额外的内环建议并获得一个小噪音近似值。 我们的方法计算成本可以通过对其余的内环应用拉普尔近似值来进一步降低。 因此, 我们提出两种方法, 小噪音双环蒙特卡洛和小鼻子蒙特卡洛拉贝特方法。 此外, 我们证明这两种方法的总复杂性仍然与案件相似, 没有干扰性不确定性。 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材料的电阻摄像实验的局部差异方程。