论文标题
Gibbs采样器的几何形状登山表的贝叶斯回归回归
Geometric ergodicity of Gibbs samplers for Bayesian error-in-variable regression
论文作者
论文摘要
多变量贝叶斯误差（EIV）线性回归被认为是在功能和响应中的其他添加剂高斯错误。使用具有独立正常和逆宽性先验的经典和伯克森错误的多元EIV回归模型构建了3变量的确定性扫描Gibbs采样器。事实证明，这些Gibbs采样器始终是千古的，可确保来自马尔可夫链的中心限制定理。我们通过模拟数据来证明Gibbs采样器的优势和局限性，以解决大型数据问题，鲁棒性的指定性，还分析了天体物理学中的真实数据示例。
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.
