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Discussing the “big n problem”

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  • Giovanna Jona Lasinio
  • Gianluca Mastrantonio
  • Alessio Pollice

Abstract

When a large amount of spatial data is available computational and modeling challenges arise and they are often labeled as “big n problem”. In this work we present a brief review of the literature. Then we focus on two approaches, respectively based on stochastic partial differential equations and integrated nested Laplace approximation, and on the tapering of the spatial covariance matrix. The fitting and predictive abilities of using the two methods in conjunction with Kriging interpolation are compared in a simulation study. Copyright Springer-Verlag 2013

Suggested Citation

  • Giovanna Jona Lasinio & Gianluca Mastrantonio & Alessio Pollice, 2013. "Discussing the “big n problem”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(1), pages 97-112, March.
    • Handle: RePEc:spr:stmapp:v:22:y:2013:i:1:p:97-112
    DOI: 10.1007/s10260-012-0207-2
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    References listed on IDEAS

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    1. Sudipto Banerjee & Alan E. Gelfand & Andrew O. Finley & Huiyan Sang, 2008. "Gaussian predictive process models for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 825-848, September.
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    5. Kaufman, Cari G. & Schervish, Mark J. & Nychka, Douglas W., 2008. "Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1545-1555.
    6. Zhang, Hao, 2004. "Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 250-261, January.
    7. Hååvard Rue & Hååkon Tjelmeland, 2002. "Fitting Gaussian Markov Random Fields to Gaussian Fields," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 31-49, March.
    8. 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.
    9. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
    10. Finley, Andrew O. & Sang, Huiyan & Banerjee, Sudipto & Gelfand, Alan E., 2009. "Improving the performance of predictive process modeling for large datasets," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2873-2884, June.
    11. Noel Cressie & Gardar Johannesson, 2008. "Fixed rank kriging for very large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 209-226, February.
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    1. Zaouche, Mounia & Bode, Nikolai W.F., 2023. "Bayesian spatio-temporal models for mapping urban pedestrian traffic," Journal of Transport Geography, Elsevier, vol. 111(C).

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