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Bayesian inference for generalized additive mixed models based on Markov random field priors
Author(s) -
Fahrmeir Ludwig,
Lang Stefan
Publication year - 2001
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 - 10.1111/1467-9876.00229
Subject(s) - covariate , random effects model , markov chain monte carlo , prior probability , econometrics , bayesian probability , overdispersion , inference , bayesian inference , markov chain , semiparametric regression , mathematics , markov random field , computer science , statistics , count data , nonparametric statistics , artificial intelligence , poisson distribution , medicine , meta analysis , segmentation , image segmentation
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.