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Extending Integrated Nested Laplace Approximation to a Class of Near‐Gaussian Latent Models
Author(s) -
Martins Thiago G.,
Rue Håvard
Publication year - 2014
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12073
Subject(s) - laplace's method , gaussian , mathematics , markov chain , extension (predicate logic) , laplace transform , markov chain monte carlo , component (thermodynamics) , latent class model , flexibility (engineering) , computer science , algorithm , mathematical optimization , theoretical computer science , monte carlo method , statistics , mathematical analysis , physics , quantum mechanics , thermodynamics , programming language
This work extends the integrated nested Laplace approximation (INLA) method to latent models outside the scope of latent Gaussian models, where independent components of the latent field can have a near‐Gaussian distribution. The proposed methodology is an essential component of a bigger project that aims to extend the R package INLA in order to allow the user to add flexibility and challenge the Gaussian assumptions of some of the model components in a straightforward and intuitive way. Our approach is applied to two examples, and the results are compared with that obtained by Markov chain Monte Carlo, showing similar accuracy with only a small fraction of computational time. Implementation of the proposed extension is available in the R‐INLA package.