论文标题
贝叶斯最佳实验设计中预期效用的稳定性估算
Stability estimates for the expected utility in Bayesian optimal experimental design
论文作者
论文摘要
我们研究贝叶斯最佳实验设计中预期效用函数的稳定性。我们在非参数环境中为此问题提供了一个框架，并证明了相对于可能性扰动的预期效用的收敛率。该速率在设计空间上是均匀的，并且通过在特殊情况下证明了下限，可以证明其在一般环境中的清晰度。为了使问题变得更具体，我们通过考虑非线性贝叶斯的逆问题，与高斯的可能性相反，并证明对一般情况的假设得到了满足，并恢复了预期效用在观察图上的扰动方面的稳定性。在三个不同的示例中，在数值上证明了理论收敛速率。
We study stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in a non-parametric setting and prove a convergence rate of the expected utility with respect to a likelihood perturbation. This rate is uniform over the design space and its sharpness in the general setting is demonstrated by proving a lower bound in a special case. To make the problem more concrete we proceed by considering non-linear Bayesian inverse problems with Gaussian likelihood and prove that the assumptions set out for the general case are satisfied and regain the stability of the expected utility with respect to perturbations to the observation map. Theoretical convergence rates are demonstrated numerically in three different examples.
