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Bayesian inference for generalized additive mixed models based on Markov random field priors

Bayesian inference for generalized additive mixed models based on Markov random field priors Most regression problems in practice require flexible semiparametric forms of the predictor for modelling the dependence of responses on covariates. Moreover, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal or spatial data. We present a unified approach for Bayesian inference via Markov chain Monte Carlo simulation in generalized additive and semiparametric mixed models. Different types of covariates, such as the usual covariates with fixed effects, metrical covariates with non‐linear effects, unstructured random effects, trend and seasonal components in longitudinal data and spatial covariates, are all treated within the same general framework by assigning appropriate Markov random field priors with different forms and degrees of smoothness. We applied the approach in several case‐studies and consulting cases, showing that the methods are also computationally feasible in problems with many covariates and large data sets. In this paper, we choose two typical applications. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the Royal Statistical Society: Series C (Applied Statistics) Wiley

Bayesian inference for generalized additive mixed models based on Markov random field priors

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References (41)

Publisher
Wiley
Copyright
Copyright © 2001 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0035-9254
eISSN
1467-9876
DOI
10.1111/1467-9876.00229
Publisher site
See Article on Publisher Site

Abstract

Most regression problems in practice require flexible semiparametric forms of the predictor for modelling the dependence of responses on covariates. Moreover, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal or spatial data. We present a unified approach for Bayesian inference via Markov chain Monte Carlo simulation in generalized additive and semiparametric mixed models. Different types of covariates, such as the usual covariates with fixed effects, metrical covariates with non‐linear effects, unstructured random effects, trend and seasonal components in longitudinal data and spatial covariates, are all treated within the same general framework by assigning appropriate Markov random field priors with different forms and degrees of smoothness. We applied the approach in several case‐studies and consulting cases, showing that the methods are also computationally feasible in problems with many covariates and large data sets. In this paper, we choose two typical applications.

Journal

Journal of the Royal Statistical Society: Series C (Applied Statistics)Wiley

Published: Jan 1, 2001

Keywords: ; ; ; ; ;

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