Exact sampling of the unobserved covariates in Bayesian spline models for measurement error problems

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• 作者：Anindya Bhadra ; Raymond J. Carroll
• 刊名：Statistics and Computing
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：26
• 期：4
• 页码：827-840
• 全文大小：2,605 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics Computing and Software
  Statistics
  Numeric Computing
  Mathematics
  Artificial Intelligence and Robotics
  
• 出版者：Springer Netherlands
• ISSN：1573-1375
• 卷排序：26

文摘

In truncated polynomial spline or B-spline models where the covariates are measured with error, a fully Bayesian approach to model fitting requires the covariates and model parameters to be sampled at every Markov chain Monte Carlo iteration. Sampling the unobserved covariates poses a major computational problem and usually Gibbs sampling is not possible. This forces the practitioner to use a Metropolis–Hastings step which might suffer from unacceptable performance due to poor mixing and might require careful tuning. In this article we show for the cases of truncated polynomial spline or B-spline models of degree equal to one, the complete conditional distribution of the covariates measured with error is available explicitly as a mixture of double-truncated normals, thereby enabling a Gibbs sampling scheme. We demonstrate via a simulation study that our technique performs favorably in terms of computational efficiency and statistical performance. Our results indicate up to 62 and 54 % increase in mean integrated squared error efficiency when compared to existing alternatives while using truncated polynomial splines and B-splines respectively. Furthermore, there is evidence that the gain in efficiency increases with the measurement error variance, indicating the proposed method is a particularly valuable tool for challenging applications that present high measurement error. We conclude with a demonstration on a nutritional epidemiology data set from the NIH-AARP study and by pointing out some possible extensions of the current work.KeywordsBayesian methodsGibbs sampling Measurement error modelsNonparametric regressionTruncated normals