IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i12p3197-3217.html
   My bibliography  Save this article

Variational Bayesian methods for spatial data analysis

Author

Listed:
  • Ren, Qian
  • Banerjee, Sudipto
  • Finley, Andrew O.
  • Hodges, James S.

Abstract

With scientific data available at geocoded locations, investigators are increasingly turning to spatial process models for carrying out statistical inference. However, fitting spatial models often involves expensive matrix decompositions, whose computational complexity increases in cubic order with the number of spatial locations. This situation is aggravated in Bayesian settings where such computations are required once at every iteration of the Markov chain Monte Carlo (MCMC) algorithms. In this paper, we describe the use of Variational Bayesian (VB) methods as an alternative to MCMC to approximate the posterior distributions of complex spatial models. Variational methods, which have been used extensively in Bayesian machine learning for several years, provide a lower bound on the marginal likelihood, which can be computed efficiently. We provide results for the variational updates in several models especially emphasizing their use in multivariate spatial analysis. We demonstrate estimation and model comparisons from VB methods by using simulated data as well as environmental data sets and compare them with inference from MCMC.

Suggested Citation

  • Ren, Qian & Banerjee, Sudipto & Finley, Andrew O. & Hodges, James S., 2011. "Variational Bayesian methods for spatial data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3197-3217, December.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:12:p:3197-3217
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311002003
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. 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.
    3. Alan Gelfand & Alexandra Schmidt & Sudipto Banerjee & C. Sirmans, 2004. "Nonstationary multivariate process modeling through spatially varying coregionalization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 263-312, December.
    4. 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.
    5. Gelfand A.E. & Kim H-J. & Sirmans C.F. & Banerjee S., 2003. "Spatial Modeling With Spatially Varying Coefficient Processes," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 387-396, January.
    6. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    7. Paciorek, Christopher J., 2007. "Computational techniques for spatial logistic regression with large data sets," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3631-3653, May.
    8. 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, January.
    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


    Cited by:

    1. Volant, Stevenn & Martin Magniette, Marie-Laure & Robin, Stéphane, 2012. "Variational Bayes approach for model aggregation in unsupervised classification with Markovian dependency," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2375-2387.
    2. Lu Zhang & Sudipto Banerjee & Andrew O. Finley, 2021. "High‐dimensional multivariate geostatistics: A Bayesian matrix‐normal approach," Environmetrics, John Wiley & Sons, Ltd., vol. 32(4), June.
    3. Yin Song & Shufei Ge & Jiguo Cao & Liangliang Wang & Farouk S. Nathoo, 2022. "A Bayesian spatial model for imaging genetics," Biometrics, The International Biometric Society, vol. 78(2), pages 742-753, June.
    4. Aaron Osgood‐Zimmerman & Jon Wakefield, 2023. "A Statistical Review of Template Model Builder: A Flexible Tool for Spatial Modelling," International Statistical Review, International Statistical Institute, vol. 91(2), pages 318-342, August.
    5. F. S. Nathoo & A. Babul & A. Moiseev & N. Virji-Babul & M. F. Beg, 2014. "A variational Bayes spatiotemporal model for electromagnetic brain mapping," Biometrics, The International Biometric Society, vol. 70(1), pages 132-143, March.
    6. Shinichiro Shirota & Andrew O. Finley & Bruce D. Cook & Sudipto Banerjee, 2023. "Conjugate sparse plus low rank models for efficient Bayesian interpolation of large spatial data," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    7. Bansal, Prateek & Krueger, Rico & Graham, Daniel J., 2021. "Fast Bayesian estimation of spatial count data models," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andrew O. Finley & Sudipto Banerjee & Patrik Waldmann & Tore Ericsson, 2009. "Hierarchical Spatial Modeling of Additive and Dominance Genetic Variance for Large Spatial Trial Datasets," Biometrics, The International Biometric Society, vol. 65(2), pages 441-451, June.
    2. Liang, Shengde & Banerjee, Sudipto & Bushhouse, Sally & Finley, Andrew O. & Carlin, Bradley P., 2008. "Hierarchical multiresolution approaches for dense point-level breast cancer treatment data," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2650-2668, January.
    3. Eidsvik, Jo & Finley, Andrew O. & Banerjee, Sudipto & Rue, Håvard, 2012. "Approximate Bayesian inference for large spatial datasets using predictive process models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1362-1380.
    4. Congdon, Peter, 2006. "A model for non-parametric spatially varying regression effects," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 422-445, January.
    5. 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.
    6. Hossein Boojari & Majid Khaledi & Firoozeh Rivaz, 2016. "A non-homogeneous skew-Gaussian Bayesian spatial model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 55-73, March.
    7. Hossain, Md. Monir & Lawson, Andrew B., 2009. "Approximate methods in Bayesian point process spatial models," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2831-2842, June.
    8. Litvinenko, Alexander & Sun, Ying & Genton, Marc G. & Keyes, David E., 2019. "Likelihood approximation with hierarchical matrices for large spatial datasets," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 115-132.
    9. Qian Ren & Sudipto Banerjee, 2013. "Hierarchical Factor Models for Large Spatially Misaligned Data: A Low-Rank Predictive Process Approach," Biometrics, The International Biometric Society, vol. 69(1), pages 19-30, March.
    10. Andrew Finley & Sudipto Banerjee & Alan Gelfand, 2012. "Bayesian dynamic modeling for large space-time datasets using Gaussian predictive processes," Journal of Geographical Systems, Springer, vol. 14(1), pages 29-47, January.
    11. White, Gentry & Ghosh, Sujit K., 2009. "A stochastic neighborhood conditional autoregressive model for spatial data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3033-3046, June.
    12. David Wheeler & Catherine Calder, 2007. "An assessment of coefficient accuracy in linear regression models with spatially varying coefficients," Journal of Geographical Systems, Springer, vol. 9(2), pages 145-166, June.
    13. Alexandra Schmidt & Ajax Moreira & Steven Helfand & Thais Fonseca, 2009. "Spatial stochastic frontier models: accounting for unobserved local determinants of inefficiency," Journal of Productivity Analysis, Springer, vol. 31(2), pages 101-112, April.
    14. Zhang, Shen & Liu, Xin & Tang, Jinjun & Cheng, Shaowu & Qi, Yong & Wang, Yinhai, 2018. "Spatio-temporal modeling of destination choice behavior through the Bayesian hierarchical approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 537-551.
    15. C Emi Fergus & Andrew O Finley & Patricia A Soranno & Tyler Wagner, 2016. "Spatial Variation in Nutrient and Water Color Effects on Lake Chlorophyll at Macroscales," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-20, October.
    16. Joaquim Henriques Vianna Neto & Alexandra M. Schmidt & Peter Guttorp, 2014. "Accounting for spatially varying directional effects in spatial covariance structures," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(1), pages 103-122, January.
    17. Philip A. White & Alan E. Gelfand, 2021. "Multivariate functional data modeling with time-varying clustering," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 586-602, September.
    18. Veronica J. Berrocal & Alan E. Gelfand & David M. Holland, 2012. "Space-Time Data fusion Under Error in Computer Model Output: An Application to Modeling Air Quality," Biometrics, The International Biometric Society, vol. 68(3), pages 837-848, September.
    19. 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.
    20. Matthew J. Heaton & Abhirup Datta & Andrew O. Finley & Reinhard Furrer & Joseph Guinness & Rajarshi Guhaniyogi & Florian Gerber & Robert B. Gramacy & Dorit Hammerling & Matthias Katzfuss & Finn Lindgr, 2019. "A Case Study Competition Among Methods for Analyzing Large Spatial Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 398-425, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:55:y:2011:i:12:p:3197-3217. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.