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    Markov chain Monte Carlo with the Integrated Nested Laplace Approximation

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    Type
    Article
    Authors
    Gómez-Rubio, Virgilio cc
    Rue, Haavard cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2017-10-06
    Preprint Posting Date
    2017-01-26
    Online Publication Date
    2017-10-06
    Print Publication Date
    2018-09
    Permanent link to this record
    http://hdl.handle.net/10754/625832
    
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    Abstract
    The Integrated Nested Laplace Approximation (INLA) has established itself as a widely used method for approximate inference on Bayesian hierarchical models which can be represented as a latent Gaussian model (LGM). INLA is based on producing an accurate approximation to the posterior marginal distributions of the parameters in the model and some other quantities of interest by using repeated approximations to intermediate distributions and integrals that appear in the computation of the posterior marginals. INLA focuses on models whose latent effects are a Gaussian Markov random field. For this reason, we have explored alternative ways of expanding the number of possible models that can be fitted using the INLA methodology. In this paper, we present a novel approach that combines INLA and Markov chain Monte Carlo (MCMC). The aim is to consider a wider range of models that can be fitted with INLA only when some of the parameters of the model have been fixed. We show how new values of these parameters can be drawn from their posterior by using conditional models fitted with INLA and standard MCMC algorithms, such as Metropolis–Hastings. Hence, this will extend the use of INLA to fit models that can be expressed as a conditional LGM. Also, this new approach can be used to build simpler MCMC samplers for complex models as it allows sampling only on a limited number of parameters in the model. We will demonstrate how our approach can extend the class of models that could benefit from INLA, and how the R-INLA package will ease its implementation. We will go through simple examples of this new approach before we discuss more advanced applications with datasets taken from the relevant literature. In particular, INLA within MCMC will be used to fit models with Laplace priors in a Bayesian Lasso model, imputation of missing covariates in linear models, fitting spatial econometrics models with complex nonlinear terms in the linear predictor and classification of data with mixture models. Furthermore, in some of the examples we could exploit INLA within MCMC to make joint inference on an ensemble of model parameters.
    Citation
    Gómez-Rubio V, Rue H (2017) Markov chain Monte Carlo with the Integrated Nested Laplace Approximation. Statistics and Computing. Available: http://dx.doi.org/10.1007/s11222-017-9778-y.
    Sponsors
    Virgilio Gómez-Rubio has been supported by Grant PPIC-2014-001, funded by Consejería de Educación, Cultura y Deportes (JCCM) and FEDER, and Grant MTM2016-77501-P, funded by Ministerio de Economía y Competitividad. We would also like to thank Prof. Aki Vehtari for his comments on a preliminary version of this paper.
    Publisher
    Springer Nature
    Journal
    Statistics and Computing
    DOI
    10.1007/s11222-017-9778-y
    arXiv
    1701.07844
    Additional Links
    http://link.springer.com/article/10.1007/s11222-017-9778-y
    ae974a485f413a2113503eed53cd6c53
    10.1007/s11222-017-9778-y
    Scopus Count
    Collections
    Articles; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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