Multivariate Bayesian error-in-variable (EIV) linear regression is considered to account for additional additive Gaussian error in the features and response. A 3-variable deterministic scan Gibbs samplers is constructed for multivariate EIV regression models using classical and Berkson errors with independent normal and inverse-Wishart priors. These Gibbs samplers are proven to always be geometrically ergodic which ensures a central limit theorem for many time averages from the Markov chains. We demonstrate the strengths and limitations of the Gibbs sampler with simulated data for large data problems, robustness to misspecification and also analyze a real-data example in astrophysics.

翻译：考虑多元贝叶斯变量含误差(EIV)线性回归模型，以解释特征和响应中额外的加性高斯误差。针对经典误差和伯克森误差，采用独立正态分布和逆威沙特先验分布，构建了多元EIV回归模型的3变量确定性扫描吉布斯采样器。证明这些吉布斯采样器始终具有几何遍历性，从而确保马尔可夫链的许多时间平均满足中心极限定理。我们通过模拟数据展示了吉布斯采样器在大规模数据问题中的优势与局限、对错误设定的鲁棒性，并分析了天体物理学中的一个真实数据实例。