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Bayesian analysis of measurement error models using integrated nested Laplace approximations
Author(s) -
Muff Stefanie,
Riebler Andrea,
Held Leonhard,
Rue Håvard,
Saner Philippe
Publication year - 2015
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/rssc.12069
Subject(s) - laplace's method , laplace transform , computer science , mathematics , bayesian probability , bayesian inference , algorithm , gaussian , inference , statistical inference , artificial intelligence , statistics , mathematical analysis , physics , quantum mechanics
Summary 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.