用改进的贝叶斯方法设计实验，让结果更抗干扰。
Robust Experimental Design via Generalised Bayesian Inference
- 用损失函数替代似然函数，提升模型错误时的鲁棒性
- 提出新指标Gibbs EIG，能有效应对异常值和噪声误设
- 适合噪声分布不确定或数据含异常的实验设计场景
贝叶斯最优实验设计是一种基于贝叶斯推断的严谨框架，可量化特定实验设计所能带来的信息增益。但其准确性依赖于数据生成模型正确设定这一假设。若该假设不成立，传统贝叶斯方法可能导致不良推断和信息增益估计。广义贝叶斯（或吉布斯）推断是一种更鲁棒的概率推断框架，它在贝叶斯更新中以适当的损失函数替代似然函数。本文提出广义贝叶斯最优实验设计（GBOED），将吉布斯推断扩展至实验设计领域，实现了设计与推断双重鲁棒性。通过扩展的信息论框架，我们推导出新的获取函数——吉布斯期望信息增益（Gibbs EIG）。实证结果表明，GBOED在应对异常值及对结果噪声分布的错误假设方面显著增强鲁棒性。
原文摘要 · Abstract (English)
Bayesian optimal experimental design is a principled framework for conducting experiments that leverages Bayesian inference to quantify how much information one can expect to gain from selecting a certain design. However, accurate Bayesian inference relies on the assumption that one's statistical model of the data-generating process is correctly specified. If this assumption is violated, Bayesian methods can lead to poor inference and estimates of information gain. Generalised Bayesian (or Gibbs) inference is a more robust probabilistic inference framework that replaces the likelihood in the Bayesian update by a suitable loss function. In this work, we present Generalised Bayesian Optimal Experimental Design (GBOED), an extension of Gibbs inference to the experimental design setting which achieves robustness in both design and inference. Using an extended information-theoretic framework, we derive a new acquisition function, the Gibbs expected information gain (Gibbs EIG). Our empirical results demonstrate that GBOED enhances robustness to outliers and incorrect assumptions about the outcome noise distribution.
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