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Authors = Roger S. Bivand ORCID = 0000-0003-2392-6140

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23 pages, 1179 KiB  
Article
Estimating Spatial Econometrics Models with Integrated Nested Laplace Approximation
by Virgilio Gómez-Rubio, Roger S. Bivand and Håvard Rue
Mathematics 2021, 9(17), 2044; https://doi.org/10.3390/math9172044 - 25 Aug 2021
Cited by 17 | Viewed by 4158
Abstract
The integrated nested Laplace approximation (INLA) provides a fast and effective method for marginal inference in Bayesian hierarchical models. This methodology has been implemented in the R-INLA package which permits INLA to be used from within R statistical software. Although INLA is implemented [...] Read more.
The integrated nested Laplace approximation (INLA) provides a fast and effective method for marginal inference in Bayesian hierarchical models. This methodology has been implemented in the R-INLA package which permits INLA to be used from within R statistical software. Although INLA is implemented as a general methodology, its use in practice is limited to the models implemented in the R-INLA package. Spatial autoregressive models are widely used in spatial econometrics but have until now been lacking from the R-INLA package. In this paper, we describe the implementation and application of a new class of latent models in INLA made available through R-INLA. This new latent class implements a standard spatial lag model. The implementation of this latent model in R-INLA also means that all the other features of INLA can be used for model fitting, model selection and inference in spatial econometrics, as will be shown in this paper. Finally, we will illustrate the use of this new latent model and its applications with two data sets based on Gaussian and binary outcomes. Full article
(This article belongs to the Section D1: Probability and Statistics)
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15 pages, 1659 KiB  
Article
Bayesian Model Averaging with the Integrated Nested Laplace Approximation
by Virgilio Gómez-Rubio, Roger S. Bivand and Håvard Rue
Econometrics 2020, 8(2), 23; https://doi.org/10.3390/econometrics8020023 - 1 Jun 2020
Cited by 19 | Viewed by 6159
Abstract
The integrated nested Laplace approximation (INLA) for Bayesian inference is an efficient approach to estimate the posterior marginal distributions of the parameters and latent effects of Bayesian hierarchical models that can be expressed as latent Gaussian Markov random fields (GMRF). The representation as [...] Read more.
The integrated nested Laplace approximation (INLA) for Bayesian inference is an efficient approach to estimate the posterior marginal distributions of the parameters and latent effects of Bayesian hierarchical models that can be expressed as latent Gaussian Markov random fields (GMRF). The representation as a GMRF allows the associated software R-INLA to estimate the posterior marginals in a fraction of the time as typical Markov chain Monte Carlo algorithms. INLA can be extended by means of Bayesian model averaging (BMA) to increase the number of models that it can fit to conditional latent GMRF. In this paper, we review the use of BMA with INLA and propose a new example on spatial econometrics models. Full article
(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)
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