Bayesian analysis of measurement error models using integrated nested Laplace approximations

Stefanie Muff, Andrea Riebler, Leonhard Held*, Håvard Rue, Philippe Saner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

64 Scopus citations


To account for measurement error (ME) in explanatory variables, Bayesian approaches provide a flexible framework, as expert knowledge can be incorporated in the prior distributions. Recently, integrated nested Laplace approximations have been proven to be a computationally convenient alternative to sampling approaches for Bayesian inference in latent Gaussian models. We show how the most common approaches to adjust for ME, the classical and the Berkson ME, fit into this framework. This is achieved through a reformulation with augmented pseudo-observations and a suitable extension of the latent Gaussian field. Two specific classes are described, which allow for a particularly simple implementation using integrated nested Laplace approximations. We present three applications within the framework of generalized linear (mixed) models with ME. To illustrate the practical feasibility, R code is provided in on-line supplementary material.

Original languageEnglish (US)
Pages (from-to)231-252
Number of pages22
JournalJournal of the Royal Statistical Society. Series C: Applied Statistics
Issue number2
StatePublished - Feb 1 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014 Royal Statistical Society.


  • Bayesian analysis
  • Berkson error
  • Classical error
  • Integrated nested Laplace approximation
  • Measurement error

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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