AI 中文总结
针对计数数据模型贝叶斯数据增强算法的效率问题，提出边际数据增强方法，通过重新缩放零计数观测的潜在结果减轻后验依赖性，经合成数据、模拟研究及人口统计应用验证了该方法能提高采样效率及具有广泛适用性。
AI 中文摘要
计数数据模型在许多领域普遍存在，但此类模型的贝叶斯数据增强算法在马尔可夫链蒙特卡罗效率方面常遇挑战。后验模拟在处理大量零结果数据时尤其困难。本文引入边际数据增强方法用于半参数贝叶斯计数数据回归模型，基于一个工作参数对零计数观测对应的潜在结果进行重新缩放。该策略减轻了通常会降低标准数据增强方案效率的强后验依赖性，提高了采样效率。通过合成数据示例和模拟研究证明了与传统采样方法相比混合效果的改进。奥地利的人口统计应用进一步强调了该方法的广泛适用性。
英文摘要
Count data models are ubiquitous in many fields, yet Bayesian data augmentation algorithms for such models frequently encounter challenges with Markov chain Monte Carlo efficiency. Posterior simulation is especially demanding when modeling data with a high proportion of zero outcomes. In this paper, we address this issue by introducing a marginal data augmentation approach for semi-parametric Bayesian count data regression models, based on a working parameter that rescales latent outcomes corresponding to zero-count observations. This strategy alleviates the strong posterior dependencies that typically reduce the efficiency of standard data augmentation schemes and leads to substantial gains in sampling efficiency. Synthetic data examples and simulation studies are used to demonstrate the improvements in mixing compared to conventional sampling methods. A demographic application using latent factor analysis to model subnational mortality counts in Austria further underscores the broader applicability of the proposed methodology.
Journal refIn: Nagler, T., Kurowicka, D., Cooke, R., Joe, H. (eds), Statistical Dependence Modeling, Springer, Cham, 2026
DOI：10.1007/978-3-032-14252-8_15
