针对混合域数据的未归一化模型的鲁棒贝叶斯推断
Robust Bayesian Inference for Unnormalized Models with Mixed-Domain Data
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中文总结 AI 辅助
针对混合域未归一化模型的鲁棒贝叶斯推断难题，提出SME-BETEL半参数贝叶斯框架，证明其理论性质并通过模拟和臭氧监测应用验证了方法的有效性。
中文摘要 AI 辅助
许多统计模型涉及依赖参数的归一化常数，这些常数在计算上难以处理，给标准贝叶斯推断带来了重大障碍。尽管现有的基于似然的算法通常可以规避这些常数，但在模型误设情况下，它们的不确定性量化可能校准不佳。为应对这些挑战，我们提出SME-BETEL，这是一种半参数贝叶斯框架，将得分匹配估计方程与贝叶斯指数倾斜经验似然相结合。由此得到的后验分布无需评估归一化常数，也不需要学习率校准。我们证明了得分匹配估计量的一致性和渐近正态性，并为SME-BETEL后验分布证明了伯恩斯坦-冯·米塞斯定理。这些结果表明，SME-BETEL可信集在渐近上校准至得分匹配估计量的抽样变异性，在模型误设情况下产生有效的频率覆盖。我们进一步开发了一种针对混合域数据的新型得分匹配准则，将SME-BETEL扩展至观测值包含不同样本空间分量的模型。该构造实现了对混合域双难处理模型的鲁棒贝叶斯推断，包括具有难处理空间归一化积分的优先采样模型。模拟研究表明，SME-BETEL在模型正确设定下仍具有竞争力，在模型误设下则显著提升了不确定性量化。臭氧监测应用进一步证明了混合域构造在空间优先建模中的实用性。
英文摘要
Many statistical models involve parameter-dependent normalizing constants that are computationally intractable, creating substantial obstacles to standard Bayesian inference. Although existing likelihood-based algorithms can often circumvent these constants, their uncertainty quantification may be poorly calibrated under model misspecification. To address these challenges, we propose SME-BETEL, a semiparametric Bayesian framework that combines score matching estimating equations with Bayesian exponentially tilted empirical likelihood. The resulting posterior avoids evaluation of normalizing constants and does not require learning-rate calibration. Building on this framework, we develop a new score matching criterion for mixed-domain data, extending SME-BETEL to models whose observations combine components from different sample spaces. This construction enables robust Bayesian inference for mixed-domain doubly-intractable models. We establish consistency and asymptotic normality of the score matching estimator, and prove a Bernstein-von Mises theorem for the SME-BETEL posterior. These results show that SME-BETEL credible sets are asymptotically calibrated to the sampling variability of the score matching estimator, yielding valid frequentist coverage under model misspecification. Simulation studies show that SME-BETEL remains competitive under correct specification and substantially improves uncertainty quantification under misspecification. An ozone-monitoring application demonstrates the practical utility of the mixed-domain construction for spatial preferential modeling.
发表机构
- Texas A&M University（德克萨斯农工大学）
- University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
机构由 AI 辅助整理，请以论文原文为准。
