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Spatial Data Analysis with R-INLA with Some Extensions

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  • Bivand, Roger
  • Gómez-Rubio, Virgilio
  • Rue, Håvard

Abstract

The integrated nested Laplace approximation (INLA) provides an interesting way of approximating the posterior marginals of a wide range of Bayesian hierarchical models. This approximation is based on conducting a Laplace approximation of certain functions and numerical integration is extensively used to integrate some of the models parameters out. The R-INLA package offers an interface to INLA, providing a suitable framework for data analysis. Although the INLA methodology can deal with a large number of models, only the most relevant have been implemented within R-INLA. However, many other important models are not available for R-INLA yet. In this paper we show how to fit a number of spatial models with R-INLA, including its interaction with other R packages for data analysis. Secondly, we describe a novel method to extend the number of latent models available for the model parameters. Our approach is based on conditioning on one or several model parameters and fit these conditioned models with R-INLA. Then these models are combined using Bayesian model averaging to provide the final approximations to the posterior marginals of the model. Finally, we show some examples of the application of this technique in spatial statistics. It is worth noting that our approach can be extended to a number of other fields, and not only spatial statistics.

Suggested Citation

  • Bivand, Roger & Gómez-Rubio, Virgilio & Rue, Håvard, 2015. "Spatial Data Analysis with R-INLA with Some Extensions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i20).
    • Handle: RePEc:jss:jstsof:v:063:i20
    DOI: http://hdl.handle.net/10.18637/jss.v063.i20
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    15. Virgilio Gómez-Rubio & Roger S. Bivand & Håvard Rue, 2021. "Estimating Spatial Econometrics Models with Integrated Nested Laplace Approximation," Mathematics, MDPI, vol. 9(17), pages 1-23, August.
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    18. I. Gede Nyoman Mindra Jaya & Budhi Handoko & Yudhie Andriyana & Anna Chadidjah & Farah Kristiani & Mila Antikasari, 2023. "Multivariate Bayesian Semiparametric Regression Model for Forecasting and Mapping HIV and TB Risks in West Java, Indonesia," Mathematics, MDPI, vol. 11(17), pages 1-23, August.
    19. Darren J. Mayne & Geoffrey G. Morgan & Bin B. Jalaludin & Adrian E. Bauman, 2018. "Does Walkability Contribute to Geographic Variation in Psychosocial Distress? A Spatial Analysis of 91,142 Members of the 45 and Up Study in Sydney, Australia," IJERPH, MDPI, vol. 15(2), pages 1-24, February.
    20. Pebesma, Edzer & Bivand, Roger & Ribeiro, Paulo Justiniano, 2015. "Software for Spatial Statistics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i01).
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