论文标题
贝叶斯鲁棒多元线性回归的数据增强算法的收敛分析，数据不完整
Convergence Analysis of Data Augmentation Algorithms for Bayesian Robust Multivariate Linear Regression with Incomplete Data
论文作者
论文摘要
高斯混合物通常用于在稳健线性回归中对重尾误差分布进行建模。将多元鲁棒线性回归模型与标准不正确的先验分布相结合的可能性结合了可以使用数据增强算法进行采样的分析性棘手的后验分布。当响应矩阵缺少条目时，对算法的收敛属性的应用和分析存在独特的挑战。当不完整的数据具有“单调”结构时，提供了几何达丝的条件。在没有单调结构的情况下，对于实施算法是必需的。在这种情况下，我们提供了足够的条件，使算法成为Harris Ergodic。最后，我们表明，当有单调结构和中间插补是不必要的时，中间的插补会减慢基础蒙特卡洛马尔可夫链的收敛性，而事后插补则不会。提供了用于数据增强算法的R软件包。
Gaussian mixtures are commonly used for modeling heavy-tailed error distributions in robust linear regression. Combining the likelihood of a multivariate robust linear regression model with a standard improper prior distribution yields an analytically intractable posterior distribution that can be sampled using a data augmentation algorithm. When the response matrix has missing entries, there are unique challenges to the application and analysis of the convergence properties of the algorithm. Conditions for geometric ergodicity are provided when the incomplete data have a "monotone" structure. In the absence of a monotone structure, an intermediate imputation step is necessary for implementing the algorithm. In this case, we provide sufficient conditions for the algorithm to be Harris ergodic. Finally, we show that, when there is a monotone structure and intermediate imputation is unnecessary, intermediate imputation slows the convergence of the underlying Monte Carlo Markov chain, while post hoc imputation does not. An R package for the data augmentation algorithm is provided.
