In this paper, we analyze the convergence rate of a collapsed Gibbs sampler for crossed random effects models. Our results apply to a substantially larger range of models than previous works, including models that incorporate missingness mechanism and unbalanced level data. The theoretical tools involved in our analysis include a connection between relaxation time and autoregression matrix, concentration inequalities, and random matrix theory.
翻译:在本文中,我们分析了崩溃的Gibbs随机效应模型采样器对跨随机效应模型的趋同率。 我们的结果适用于比以往工作范围大得多的模型,包括包含缺失机制和不平衡水平数据的模型。 我们分析所涉及的理论工具包括放松时间和自动回归矩阵、集中不平等和随机矩阵理论之间的联系。