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:考虑多元贝叶斯误差-变量(EIV)线性回归,以解决特征和响应中额外的加性高斯误差。使用独立的正态和逆-Wishart先验联合考虑了经典误差和Berkson误差的多元EIV回归模型的3个变量确定性扫描Gibbs 抽样器。证明了这些Gibbs抽样器始终具有几何遍历性,从而确保了来自马尔可夫链的许多时间平均的中心极限定理。我们通过模拟大数据问题的数据、对误差规定的兼容性进行了演示,并在天文物理学中分析了一个实际数据示例。