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Bayesian Model Averaging with the Integrated Nested Laplace Approximation

Author

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  • Virgilio Gómez-Rubio

    (Department of Mathematics, School of Industrial Engineering, Universidad de Castilla-La Mancha, E-02071 Albacete, Spain
    Current address: Department of Mathematics, School of Industrial Engineering, Universidad de Castilla-La Mancha, Avda. España s/n, 02071 Albacete, Spain.
    These authors contributed equally to this work.)

  • Roger S. Bivand

    (Department of Economics, Norwegian School of Economics, 5045 Bergen, Norway
    These authors contributed equally to this work.)

  • Håvard Rue

    (CEMSE Division, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
    These authors contributed equally to this work.)

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 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.

Suggested Citation

  • Virgilio Gómez-Rubio & Roger S. Bivand & Håvard Rue, 2020. "Bayesian Model Averaging with the Integrated Nested Laplace Approximation," Econometrics, MDPI, vol. 8(2), pages 1-15, June.
    • Handle: RePEc:gam:jecnmx:v:8:y:2020:i:2:p:23-:d:365956
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    References listed on IDEAS

    as
    1. Bivand, Roger & Piras, Gianfranco, 2015. "Comparing Implementations of Estimation Methods for Spatial Econometrics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i18).
    2. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    3. Solmaria Halleck Vega & J. Paul Elhorst, 2015. "The Slx Model," Journal of Regional Science, Wiley Blackwell, vol. 55(3), pages 339-363, June.
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    Cited by:

    1. John M. Humphreys & Robert B. Srygley & David H. Branson, 2022. "Geographic Variation in Migratory Grasshopper Recruitment under Projected Climate Change," Geographies, MDPI, vol. 2(1), pages 1-19, January.
    2. Zongyuan Xia & Bo Tang & Long Qin & Huiguo Zhang & Xijian Hu, 2023. "Spatially Dependent Bayesian Modeling of Geostatistics Data and Its Application for Tuberculosis (TB) in China," Mathematics, MDPI, vol. 11(19), pages 1-15, October.
    3. 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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