Advanced Search
MyIDEAS: Login to save this article or follow this journal

Approximate Bayesian inference for large spatial datasets using predictive process models

Contents:

Author Info

  • Eidsvik, Jo
  • Finley, Andrew O.
  • Banerjee, Sudipto
  • Rue, Håvard
Registered author(s):

    Abstract

    The challenges of estimating hierarchical spatial models to large datasets are addressed. With the increasing availability of geocoded scientific data, hierarchical models involving spatial processes have become a popular method for carrying out spatial inference. Such models are customarily estimated using Markov chain Monte Carlo algorithms that, while immensely flexible, can become prohibitively expensive. In particular, fitting hierarchical spatial models often involves expensive decompositions of dense matrices whose computational complexity increases in cubic order with the number of spatial locations. Such matrix computations are required in each iteration of the Markov chain Monte Carlo algorithm, rendering them infeasible for large spatial datasets. The computational challenges in analyzing large spatial datasets are considered by merging two recent developments. First, the predictive process model is used as a reduced-rank spatial process, to diminish the dimensionality of the model. Then a computational framework is developed for estimating predictive process models using the integrated nested Laplace approximation. The settings where the first stage likelihood is Gaussian or non-Gaussian are discussed. Issues such as predictions and model comparisons are also discussed. Results are presented for synthetic data and several environmental datasets.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311003938
    Download Restriction: Full text for ScienceDirect subscribers only.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 6 ()
    Pages: 1362-1380

    as in new window
    Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1362-1380

    Contact details of provider:
    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Approximate Bayesian inference; Computational statistics; Gaussian processes; Geostatistics; Laplace approximation; Predictive process model;

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    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.
    2. E. E. Kammann & M. P. Wand, 2003. "Geoadditive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 1-18.
    3. Crainiceanu, Ciprian M. & Diggle, Peter J. & Rowlingson, Barry, 2008. "Bivariate Binomial Spatial Modeling of Loa loa Prevalence in Tropical Africa," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 21-37, March.
    4. Michael L. Stein & Zhiyi Chi & Leah J. Welty, 2004. "Approximating likelihoods for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 275-296.
    5. H�vard 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.
    6. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    7. 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.
    8. Varin, Cristiano & Host, Gudmund & Skare, Oivind, 2005. "Pairwise likelihood inference in spatial generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1173-1191, June.
    9. Banerjee, Sudipto & Finley, Andrew O. & Waldmann, Patrik & Ericsson, Tore, 2010. "Hierarchical Spatial Process Models for Multiple Traits in Large Genetic Trials," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 506-521.
    10. Fuentes, Montserrat, 2007. "Approximate Likelihood for Large Irregularly Spaced Spatial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 321-331, March.
    11. Peter Diggle & Søren Lophaven, 2006. "Bayesian Geostatistical Design," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 33(1), pages 53-64.
    12. Ainsworth, L.M. & Dean, C.B., 2006. "Approximate inference for disease mapping," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2552-2570, June.
    13. 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.
    14. Jo Eidsvik & Sara Martino & H�Vard Rue, 2009. "Approximate Bayesian Inference in Spatial Generalized Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 36(1), pages 1-22.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as in new window

    Cited by:
    1. Jun, Mikyoung, 2014. "Matérn-based nonstationary cross-covariance models for global processes," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 134-146.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1362-1380. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.