Markov Chain Monte Carlo with the Integrated Nested Laplace\n Approximation

2017/01/26 by Virgilio Gómez‐Rubio, Håvard Rue, Gómez-Rubio, Virgilio +1 · 3 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1701.07844

openalex publication_date 2017/01/26 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

The Integrated Nested Laplace Approximation (INLA) has established itself as\na widely used method for approximate inference on Bayesian hierarchical models\nwhich can be represented as a latent Gaussian model (LGM). INLA is based on\nproducing an accurate approximation to the posterior marginal distributions of\nthe parameters in the model and some other quantities of interest by using\nrepeated approximations to intermediate distributions and integrals that appear\nin the computation of the posterior marginals.\n INLA focuses on models whose latent effects are a Gaussian Markov random\nfield (GMRF). For this reason, we have explored alternative ways of expanding\nthe number of possible models that can be fitted using the INLA methodology. In\nthis paper, we present a novel approach that combines INLA and Markov chain\nMonte Carlo (MCMC). The aim is to consider a wider range of models that cannot\nbe fitted with INLA unless some of the parameters of the model have been fixed.\nHence, conditioning on these parameters the model could be fitted with the\nR-INLA package. We show how new values of these parameters can be drawn from\ntheir posterior by using conditional models fitted with INLA and standard MCMC\nalgorithms, such as Metropolis-Hastings. Hence, this will extend the use of\nINLA to fit models that can be expressed as a conditional LGM. Also, this new\napproach can be used to build simpler MCMC samplers for complex models as it\nallows sampling only on a limited number parameters in the model.\n We will demonstrate how our approach can extend the class of models that\ncould benefit from INLA, and how the R-INLA package will ease its\nimplementation. We will go through simple examples of this new approach before\nwe discuss more advanced problems with datasets taken from relevant literature.\n

Citations

• mice: Multivariate Imputation by Chained Equations inR
• Monte Carlo sampling methods using Markov chains and their applications

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