标题： 基于Wasserstein信息准则的贝叶斯最优实验设计 显示英文标题

标题： Bayesian optimal experimental design with Wasserstein information criteria

摘要： 贝叶斯最优实验设计（OED）为在实验中选择最有信息量的观测设置提供了一个合理框架。随着计算能力的迅速提升，贝叶斯OED在涉及大规模模拟的推断问题中变得越来越可行，并在反问题等领域引起了越来越多的关注。在本文中，我们引入了一种基于先验分布和后验分布之间预期Wasserstein-$p$距离的新设计准则。特别是，对于$p=2$，该准则与广泛使用的预期信息增益（EIG）有关键的相似之处，后者依赖于Kullback-Leibler散度。首先，Wasserstein-2准则在高斯回归中具有闭式解，这一特性也可以用于近似方案。其次，它可以解释为在将先验更新为后验时所产生运输成本的信息增益最大化。我们的主要贡献是对Wasserstein-1准则的稳定性分析，在先验或似然受到扰动的情况下提供了严格的误差分析。我们还将这项研究部分扩展到Wasserstein-2准则。特别是，这些结果在使用先验的实证近似时给出了误差率。最后，我们展示了Wasserstein-2准则的可计算性，并通过模拟展示了我们的近似率。 显示英文摘要

摘要： Bayesian optimal experimental design (OED) provides a principled framework for selecting the most informative observational settings in experiments. With rapid advances in computational power, Bayesian OED has become increasingly feasible for inference problems involving large-scale simulations, attracting growing interest in fields such as inverse problems. In this paper, we introduce a novel design criterion based on the expected Wasserstein-$p$ distance between the prior and posterior distributions. Especially, for $p=2$, this criterion shares key parallels with the widely used expected information gain (EIG), which relies on the Kullback--Leibler divergence instead. First, the Wasserstein-2 criterion admits a closed-form solution for Gaussian regression, a property which can be also leveraged for approximative schemes. Second, it can be interpreted as maximizing the information gain measured by the transport cost incurred when updating the prior to the posterior. Our main contribution is a stability analysis of the Wasserstein-1 criterion, where we provide a rigorous error analysis under perturbations of the prior or likelihood. We partially extend this study also to the Wasserstein-2 criterion. In particular, these results yield error rates when empirical approximations of priors are used. Finally, we demonstrate the computability of the Wasserstein-2 criterion and demonstrate our approximation rates through simulations.