Polynomial chaos expansions (PCE) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully Bayesian formulations remain rare, especially with implementations in R. Motivated by the success of adaptive Bayesian machine learning models such as BART, BASS, and BPPR, we develop a new fully Bayesian adaptive PCE method with an efficient and accessible R implementation: khaos. Our approach includes a novel proposal distribution that enables data-driven interaction selection, and supports a modified g-prior tailored to PCE structure. Through simulation studies and real-world UQ applications, we demonstrate that Bayesian adaptive PCE provides competitive performance for surrogate modeling, global sensitivity analysis, and ordinal regression tasks.

翻译：多项式混沌展开（PCE）在不确定性量化（UQ）任务中广泛应用，特别是在应用数学领域。然而，PCE在统计学文献中受到的关注相对较少，完全贝叶斯形式的实现尤为罕见，尤其是在R语言中的实现。受BART、BASS和BPPR等自适应贝叶斯机器学习模型成功的启发，我们开发了一种新的完全贝叶斯自适应PCE方法，并提供了高效且易于使用的R语言实现：khaos。我们的方法包括一种新颖的提议分布，支持数据驱动的交互项选择，并针对PCE结构设计了改进的g-先验。通过模拟研究和实际UQ应用，我们证明贝叶斯自适应PCE在代理建模、全局敏感性分析和序数回归任务中具有竞争力的性能。