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A novel method of marginalisation using low discrepancy sequences for integrated nested Laplace approximations

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  • Brown, Paul T.
  • Joshi, Chaitanya
  • Joe, Stephen
  • Rue, Håvard

Abstract

Recently, it has been shown that the shape of a marginal distribution can be more accurately and efficiently captured using a set of low discrepancy sequence (LDS) points compared to standard grid points. This suggests that the use of LDS could improve the approximation to marginal posterior distributions produced by grid-based Bayesian methods such as the Integrated Nested Laplace Approximation (INLA). However, obtaining marginal posteriors using LDS is not straightforward. Two algorithms are proposed that can be incorporated into the INLA implementation to approximate marginal posterior distributions using LDS without sacrificing computational efficiency. Two examples are also presented to demonstrate that the proposed algorithms, when used inside INLA, can estimate marginal posteriors more accurately and efficiently than the grid approximation INLA employs. A distinct advantage is that these algorithms can also capture multimodal shapes that the current numerical integration free algorithm (NIFA) method used by INLA cannot.

Suggested Citation

  • Brown, Paul T. & Joshi, Chaitanya & Joe, Stephen & Rue, Håvard, 2021. "A novel method of marginalisation using low discrepancy sequences for integrated nested Laplace approximations," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:csdana:v:157:y:2021:i:c:s0167947320302383
    DOI: 10.1016/j.csda.2020.107147
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    References listed on IDEAS

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    1. Martins, Thiago G. & Simpson, Daniel & Lindgren, Finn & Rue, Håvard, 2013. "Bayesian computing with INLA: New features," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 68-83.
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    3. Pierre L'Ecuyer & Christiane Lemieux, 2000. "Variance Reduction via Lattice Rules," Management Science, INFORMS, vol. 46(9), pages 1214-1235, September.
    4. 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.
    5. Ormerod, John T., 2011. "Grid based variational approximations," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 45-56, January.
    6. Finn Lindgren & Håvard Rue, 2008. "On the Second‐Order Random Walk Model for Irregular Locations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 691-700, December.
    7. repec:dau:papers:123456789/1906 is not listed on IDEAS
    8. Helene Roth & Stefan Lang & Helga Wagner, 2015. "Random intercept selection in structured additive regression models," Working Papers 2015-02, Faculty of Economics and Statistics, Universität Innsbruck.
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