标题： 面板数据模型中有效MCMC的收敛速率与辅助性-充分性交织策略 显示英文标题

标题： Convergence Rate of Efficient MCMC with Ancillarity-Sufficiency Interweaving Strategy for Panel Data Models

摘要： 提高马尔可夫链蒙特卡罗算法的效率对于增强贝叶斯分析中的计算速度和推断准确性至关重要。 这些改进可以通过利用充分性-辅助性交织策略（ASIS）来有效实现，这是一种实现这种优势的有效方法。 在此，我们提供了在贝叶斯分层面板数据模型中应用ASIS的第一个严格的理论证明。 渐近分析表明，当未观测异质性的先验方差与截面样本量N的乘积足够大时，潜在的个体效应可以几乎独立于其全局均值进行抽样。 这种接近独立性解释了ASIS的快速混合行为，并突显了其在现代“高”面板数据集中的适用性。 我们推导了简单的不等式来预测哪种传统的数据增强方案——充分数据增强（SA）或辅助数据增强（AA）——能产生更快的收敛。 通过交织SA和AA，ASIS实现了最优几何收敛速率，并使全局均值参数的马尔可夫链渐近独立同分布。 蒙特卡罗实验确认，即使对于小面板（例如，N=10），这种理论效率顺序仍然成立。 这些发现证实了ASIS在金融、营销和体育领域的实证成功，为将其扩展到具有更复杂协变量结构和非高斯规范的模型奠定了基础。 显示英文摘要

摘要： Improving Markov chain Monte Carlo algorithm efficiency is essential for enhancing computational speed and inferential accuracy in Bayesian analysis. These improvements can be effectively achieved using the ancillarity-sufficiency interweaving strategy (ASIS), an effective means of achieving such gains. Herein, we provide the first rigorous theoretical justification for applying ASIS in Bayesian hierarchical panel data models. Asymptotic analysis demonstrated that when the product of prior variance of unobserved heterogeneity and cross-sectional sample size N is sufficiently large, the latent individual effects can be sampled almost independently of their global mean. This near-independence accounts for ASIS's rapid mixing behavior and highlights its suitability for modern "tall" panel datasets. We derived simple inequalities to predict which conventional data augmentation scheme-sufficient augmentation (SA) or ancillary augmentation (AA)-yields faster convergence. By interweaving SA and AA, ASIS achieves optimal geometric rate of convergence and renders the Markov chain for the global mean parameter asymptotically independent and identically distributed. Monte Carlo experiment confirm that this theoretical efficiency ordering holds even for small panels (e.g., N=10). These findings confirm the empirical success of ASIS application across finance, marketing, and sports, laying the groundwork for its extension to models with more complex covariate structures and nonGaussian specifications.