Approximate Bayesian inference for large spatial datasets using predictive process models
AbstractThe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 56 (2012)
Issue (Month): 6 ()
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Web page: http://www.elsevier.com/locate/csda
Approximate Bayesian inference; Computational statistics; Gaussian processes; Geostatistics; Laplace approximation; Predictive process model;
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- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Ainsworth, L.M. & Dean, C.B., 2006. "Approximate inference for disease mapping," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2552-2570, June.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Jun, Mikyoung, 2014. "Matérn-based nonstationary cross-covariance models for global processes," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 134-146.
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