具有测量误差的半相依回归：基于马尔可夫链蒙特卡罗和均值场变分贝叶斯近似的估计
Seemingly Unrelated Regression with Measurement Error: Estimation via Markov chain Monte Carlo and Mean Field Variational Bayes Approximation
摘要：
在协变量中具有测量误差的线性回归是一个被大量研究的主题，然而，统计学/计量经济学文献几乎是沉默的估计一个多方程模型与测量误差。本文研究了协变量中含有测量误差的相依回归模型，介绍了两种新的估计方法：基于马尔可夫链蒙特卡罗技术的纯贝叶斯算法及其均值场变分贝叶斯（MFVB）近似. MFVB方法具有计算速度快的额外优势，可以处理大数据。与测量误差模型相关的问题是参数识别，并且这通过采用关于测量误差方差的先验分布来解决。该方法在多个模拟研究中表现良好，我们分析了由于数据生成过程中使用的真实未观测量的可靠性比或方差的不同值对后验估计的影响。本文进一步实现了所提出的算法在健康文献中的应用程序，并表明，建模数据中的测量误差可以提高模型拟合。
英文摘要：
Linear regression with measurement error in the covariates is a heavily studied topic, however, the statistics/econometrics literature is almost silent to estimating a multi-equation model with measurement error. This paper considers a seemingly unrelated regression model with measurement error in the covariates and introduces two novel estimation methods: a pure Bayesian algorithm (based on Markov chain Monte Carlo techniques) and its mean field variational Bayes (MFVB) approximation. The MFVB method has the added advantage of being computationally fast and can handle big data. An issue pertinent to measurement error models is parameter identification, and this is resolved by employing a prior distribution on the measurement error variance. The methods are shown to perform well in multiple simulation studies, where we analyze the impact on posterior estimates arising due to different values of reliability ratio or variance of the true unobserved quantity used in the data generating process. The paper further implements the proposed algorithms in an application drawn from the health literature and shows that modeling measurement error in the data can improve model fitting.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
