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Implementing approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations: A manual for the inla-program (2008)
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@TECHREPORT{Martino08implementingapproximate,
author = {Sara Martino and Nicolas Chopin},
title = {Implementing approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations: A manual for the inla-program},
institution = {},
year = {2008}
}
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Abstract
Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothing-spline models, state-space models, semiparametric regression, spatial and spatio-temporal models, log-Gaussian Cox-processes, geostatistical and geoadditive models. In this paper we consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form due to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, both in terms of convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations
Keyphrases
nested laplace approximation approximate bayesian inference latent gaussian model structured additive regression model posterior marginals non-gaussian response variable spatio-temporal model state-space model popular subset computational time main benefit closed form markov chain monte carlo log-gaussian cox-processes statistical application appropriate tool smoothing-spline model simplified version practical application linear model semiparametric regression geoadditive model used class routine analysis accurate approximation additive model latent field markov chain monte carlo method
