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

Bhadra, A; Carroll, RJ

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

Bhadra, A Carroll, RJ

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Publication Type:: Journal Article
Citation:: Statistics and Computing, 2016, 26 (4), pp. 827 - 840
Issue Date:: 2016-07-01

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Field	Value	Language
dc.contributor.author	Bhadra, A	en_US
dc.contributor.author	Carroll, RJ	en_US
dc.date.issued	2016-07-01	en_US
dc.identifier.citation	Statistics and Computing, 2016, 26 (4), pp. 827 - 840	en_US
dc.identifier.issn	0960-3174	en_US
dc.identifier.uri	http://hdl.handle.net/10453/118351
dc.description.abstract	© 2015, Springer Science+Business Media New York. 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.	en_US
dc.relation.ispartof	Statistics and Computing	en_US
dc.relation.isbasedon	10.1007/s11222-015-9572-7	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	Exact sampling of the unobserved covariates in Bayesian spline models for measurement error problems	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	26	en_US
utslib.for	0104 Statistics	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	26	en_US

Abstract:

© 2015, Springer Science+Business Media New York. 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.

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http://hdl.handle.net/10453/118351