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Applied Geospatial Bayesian Modeling in the Big Data Era: Challenges and Solutions

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  • Jason S. Byers

    (Social Science Research Institute, Duke University, Durham, NC 27708, USA
    These authors contributed equally to this work.)

  • Jeff Gill

    (Department of Government, Department of Mathematics & Statistics, Center for Data Science, American University, Washington, DC 20016, USA
    These authors contributed equally to this work.)

Abstract

Two important trends in applied statistics are an increased usage of geospatial models and an increased usage of big data. Naturally, there has been overlap as analysts utilize the techniques associated with each. With geospatial methods such as kriging, the computation required becomes intensive quickly, even with datasets that would not be considered huge in other contexts. In this work we describe a solution to the computational problem of estimating Bayesian kriging models with big data, Bootstrap Random Spatial Sampling (BRSS), and first provide an analytical argument that BRSS produces consistent estimates from the Bayesian spatial model. Second, with a medium-sized dataset on fracking in West Virginia, we show that bootstrap sample effects from a full-information Bayesian model are reduced with more bootstrap samples and more observations per sample as in standard bootstrapping. Third, we offer a realistic illustration of the method by analyzing campaign donors in California with a large geocoded dataset. With this solution, scholars will not be constrained in their ability to apply theoretically relevant geospatial Bayesian models when the size of the data produces computational intractability.

Suggested Citation

  • Jason S. Byers & Jeff Gill, 2022. "Applied Geospatial Bayesian Modeling in the Big Data Era: Challenges and Solutions," Mathematics, MDPI, vol. 10(21), pages 1-23, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4116-:d:963332
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    References listed on IDEAS

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    1. Hartman, Linda & Hossjer, Ola, 2008. "Fast kriging of large data sets with Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2331-2349, January.
    2. Jun Shao, 1990. "Bootstrap estimation of the asymptotic variances of statistical functionals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(4), pages 737-752, December.
    3. Wendy K. Tam Cho & James G. Gimpel, 2007. "Prospecting for (Campaign) Gold," American Journal of Political Science, John Wiley & Sons, vol. 51(2), pages 255-268, April.
    4. 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.
    5. Monogan, James E. & Gill, Jeff, 2016. "Measuring State and District Ideology with Spatial Realignment," Political Science Research and Methods, Cambridge University Press, vol. 4(1), pages 97-121, January.
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    Cited by:

    1. Dominique Makowski & Philip D. Waggoner, 2023. "Where Are We Going with Statistical Computing? From Mathematical Statistics to Collaborative Data Science," Mathematics, MDPI, vol. 11(8), pages 1-9, April.

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