We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of the well-known fact that solving the Bayesian D-optimal experimental design problem, i.e., maximizing the expected information gain, is equivalent to minimizing the log-determinant of posterior covariance operator. We focus on finite-dimensional inverse problems. However, the presentation is kept generic to facilitate extensions to infinite-dimensional inverse problems.

翻译：我们考虑带有高斯先验和加性高斯噪声模型的有限维贝叶斯线性反问题。本文旨在对以下众所周知的事实给出一个简单推导：求解贝叶斯D-最优实验设计问题（即最大化期望信息增益）等价于最小化后验协方差算子的对数行列式。我们重点关注有限维反问题。然而，本文的论述保持通用性，以便推广至无穷维反问题。