Rashomon播种退火用于因子设计中的鲁棒贝叶斯推断
Rashomon-Seeded Annealing for Robust Bayesian Inference in Factorial Designs
AI总结：
针对因子设计中模型不确定性导致的后验多模态和MCMC收敛问题，提出Rashomon播种退火方法，利用Rashomon集作为退火重要性采样的初始分布，实现无需穷举模型空间的完整后验推断。
摘要：
在因子设计中，通过贝叶斯模型平均整合模型不确定性受到可解释交互效应的组合爆炸阻碍，通常产生多模态后验，标准马尔可夫链蒙特卡罗算法遇到显著的收敛问题。我们提出一个通用计算框架，将Rashomon集（传统上因预测和可解释性而受到重视的高性能模型集合）重新用作估计完整后验的战略性“热启动”。我们的方法，Rashomon播种退火，通过将起始密度锚定在这些预先识别的高证据区域内，同时保持对整个模型空间的全局支持，来初始化退火重要性采样（AIS）。AIS校正不是将推断限制在Rashomon集并低估不确定性，而是恢复完整的后验推断，将Rashomon证书从推断截断转变为提议机制。我们使用Rashomon划分集（RPS）作为因子设计的严格认证种子构造器来演示这种方法。所得算法产生一致的自标准化后验摘要，如模型平均单元均值、可信区间和不确定性摘要，而无需穷举整个模型空间。这弥合了高证据模型发现与严格贝叶斯推断之间的差距，并概述了一种通用策略，其中任何高后验种子集都可以为基于AIS的模型平均提供计算杠杆。
英文摘要：
Integrating over model uncertainty in factorial designs via Bayesian model averaging is hindered by the combinatorial explosion of interpretable interaction effects, often yielding a multimodal posterior, where standard Markov chain Monte Carlo algorithms encounter significant convergence issues. We propose a general computational framework that repurposes Rashomon sets, collections of high-performing models traditionally valued for prediction and interpretability, as a strategic "warm start" for estimating the full posterior. Our method, Rashomon-seeded annealing, initializes annealed importance sampling (AIS) by anchoring the starting density within these pre-identified, high-evidence regions while preserving global support over the entire model space. Rather than restricting inference to the Rashomon set and understating uncertainty, the AIS correction restores full posterior inference, turning the Rashomon certificate from an inferential truncation into a proposal mechanism. We demonstrate this approach using Rashomon Partition Sets (RPS) as a rigorous, certified seed constructor for factorial designs. The resulting algorithm yields consistent self-normalized posterior summaries, such as model-averaged cell means, credible intervals, and uncertainty summaries without exhaustive enumeration of the complete model space. This bridges the gap between high-evidence model discovery and rigorous Bayesian inference, and outlines a general strategy in which any high-posterior seed set can provide computational leverage for AIS-based model averaging.
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