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Adaptive sampling for Bayesian geospatial models

Publication ,  Journal Article
Yang, H; Liu, F; Ji, C; Dunson, D
Published in: Statistics and Computing
November 1, 2014

Bayesian hierarchical modeling with Gaussian process random effects provides a popular approach for analyzing point-referenced spatial data. For large spatial data sets, however, generic posterior sampling is infeasible due to the extremely high computational burden in decomposing the spatial correlation matrix. In this paper, we propose an efficient algorithm—the adaptive griddy Gibbs (AGG) algorithm—to address the computational issues with large spatial data sets. The proposed algorithm dramatically reduces the computational complexity. We show theoretically that the proposed method can approximate the real posterior distribution accurately. The sufficient number of grid points for a required accuracy has also been derived. We compare the performance of AGG with that of the state-of-the-art methods in simulation studies. Finally, we apply AGG to spatially indexed data concerning building energy consumption.

Duke Scholars

Published In

Statistics and Computing

DOI

EISSN

1573-1375

ISSN

0960-3174

Publication Date

November 1, 2014

Volume

24

Issue

6

Start / End Page

1101 / 1110

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0104 Statistics
 

Citation

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Yang, H., Liu, F., Ji, C., & Dunson, D. (2014). Adaptive sampling for Bayesian geospatial models. Statistics and Computing, 24(6), 1101–1110. https://doi.org/10.1007/s11222-013-9422-4
Yang, H., F. Liu, C. Ji, and D. Dunson. “Adaptive sampling for Bayesian geospatial models.” Statistics and Computing 24, no. 6 (November 1, 2014): 1101–10. https://doi.org/10.1007/s11222-013-9422-4.
Yang H, Liu F, Ji C, Dunson D. Adaptive sampling for Bayesian geospatial models. Statistics and Computing. 2014 Nov 1;24(6):1101–10.
Yang, H., et al. “Adaptive sampling for Bayesian geospatial models.” Statistics and Computing, vol. 24, no. 6, Nov. 2014, pp. 1101–10. Scopus, doi:10.1007/s11222-013-9422-4.
Yang H, Liu F, Ji C, Dunson D. Adaptive sampling for Bayesian geospatial models. Statistics and Computing. 2014 Nov 1;24(6):1101–1110.
Journal cover image

Published In

Statistics and Computing

DOI

EISSN

1573-1375

ISSN

0960-3174

Publication Date

November 1, 2014

Volume

24

Issue

6

Start / End Page

1101 / 1110

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0104 Statistics