IDEAS home Printed from https://ideas.repec.org/a/wly/envmet/v35y2024i4ne2844.html
   My bibliography  Save this article

Recursive nearest neighbor co‐kriging models for big multi‐fidelity spatial data sets

Author

Listed:
  • Si Cheng
  • Bledar A. Konomi
  • Georgios Karagiannis
  • Emily L. Kang

Abstract

Big datasets are gathered daily from different remote sensing platforms. Recently, statistical co‐kriging models, with the help of scalable techniques, have been able to combine such datasets by using spatially varying bias corrections. The associated Bayesian inference for these models is usually facilitated via Markov chain Monte Carlo (MCMC) methods which present (sometimes prohibitively) slow mixing and convergence because they require the simulation of high‐dimensional random effect vectors from their posteriors given large datasets. To enable fast inference in big data spatial problems, we propose the recursive nearest neighbor co‐kriging (RNNC) model. Based on this model, we develop two computationally efficient inferential procedures: (a) the collapsed RNNC which reduces the posterior sampling space by integrating out the latent processes, and (b) the conjugate RNNC, an MCMC free inference which significantly reduces the computational time without sacrificing prediction accuracy. An important highlight of conjugate RNNC is that it enables fast inference in massive multifidelity data sets by avoiding expensive integration algorithms. The efficient computational and good predictive performances of our proposed algorithms are demonstrated on benchmark examples and the analysis of the High‐resolution Infrared Radiation Sounder data gathered from two NOAA polar orbiting satellites in which we managed to reduce the computational time from multiple hours to just a few minutes.

Suggested Citation

  • Si Cheng & Bledar A. Konomi & Georgios Karagiannis & Emily L. Kang, 2024. "Recursive nearest neighbor co‐kriging models for big multi‐fidelity spatial data sets," Environmetrics, John Wiley & Sons, Ltd., vol. 35(4), June.
  • Handle: RePEc:wly:envmet:v:35:y:2024:i:4:n:e2844
    DOI: 10.1002/env.2844
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/env.2844
    Download Restriction: no

    File URL: https://libkey.io/10.1002/env.2844?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Matthias Katzfuss & Joseph Guinness & Wenlong Gong & Daniel Zilber, 2020. "Vecchia Approximations of Gaussian-Process Predictions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(3), pages 383-414, September.
    2. Abhirup Datta & Sudipto Banerjee & Andrew O. Finley & Alan E. Gelfand, 2016. "Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 800-812, April.
    3. 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.
    4. 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.
    5. Bledar A. Konomi & Emily L. Kang & Ayat Almomani & Jonathan Hobbs, 2023. "Bayesian Latent Variable Co-kriging Model in Remote Sensing for Quality Flagged Observations," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(3), pages 423-441, September.
    6. B. A. Konomi & A. A. Hanandeh & P. Ma & E. L. Kang, 2019. "Computationally efficient nonstationary nearest‐neighbor Gaussian process models using data‐driven techniques," Environmetrics, John Wiley & Sons, Ltd., vol. 30(8), December.
    7. Pulong Ma & Georgios Karagiannis & Bledar A. Konomi & Taylor G. Asher & Gabriel R. Toro & Andrew T. Cox, 2022. "Multifidelity computer model emulation with high‐dimensional output: An application to storm surge," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(4), pages 861-883, August.
    8. Hai Nguyen & Noel Cressie & Amy Braverman, 2012. "Spatial Statistical Data Fusion for Remote Sensing Applications," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1004-1018, September.
    9. 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, May.
    10. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
    11. 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.
    12. Guinness, Joseph & Fuentes, Montserrat, 2016. "Isotropic covariance functions on spheres: Some properties and modeling considerations," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 143-152.
    13. 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.
    14. 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.
    15. Huiyan Sang & Jianhua Z. Huang, 2012. "A full scale approximation of covariance functions for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 111-132, January.
    16. Michele Peruzzi & Sudipto Banerjee & Andrew O. Finley, 2022. "Highly Scalable Bayesian Geostatistical Modeling via Meshed Gaussian Processes on Partitioned Domains," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 969-982, April.
    Full references (including those not matched with items on IDEAS)

    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. Bledar A. Konomi & Emily L. Kang & Ayat Almomani & Jonathan Hobbs, 2023. "Bayesian Latent Variable Co-kriging Model in Remote Sensing for Quality Flagged Observations," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(3), pages 423-441, September.
    2. Marchetti, Yuliya & Nguyen, Hai & Braverman, Amy & Cressie, Noel, 2018. "Spatial data compression via adaptive dispersion clustering," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 138-153.
    3. 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.
    4. Zilber, Daniel & Katzfuss, Matthias, 2021. "Vecchia–Laplace approximations of generalized Gaussian processes for big non-Gaussian spatial data," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    5. Peter A. Gao & Hannah M. Director & Cecilia M. Bitz & Adrian E. Raftery, 2022. "Probabilistic Forecasts of Arctic Sea Ice Thickness," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 280-302, June.
    6. Matthias Katzfuss & Joseph Guinness & Wenlong Gong & Daniel Zilber, 2020. "Vecchia Approximations of Gaussian-Process Predictions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(3), pages 383-414, September.
    7. Jialuo Liu & Tingjin Chu & Jun Zhu & Haonan Wang, 2022. "Large spatial data modeling and analysis: A Krylov subspace approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1115-1143, September.
    8. Jingjie Zhang & Matthias Katzfuss, 2022. "Multi-Scale Vecchia Approximations of Gaussian Processes," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(3), pages 440-460, September.
    9. Guhaniyogi, Rajarshi & Banerjee, Sudipto, 2019. "Multivariate spatial meta kriging," Statistics & Probability Letters, Elsevier, vol. 144(C), pages 3-8.
    10. 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.
    11. Caamaño-Carrillo, Christian & Bevilacqua, Moreno & López, Cristian & Morales-Oñate, Víctor, 2024. "Nearest neighbors weighted composite likelihood based on pairs for (non-)Gaussian massive spatial data with an application to Tukey-hh random fields estimation," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    12. Sameh Abdulah & Yuxiao Li & Jian Cao & Hatem Ltaief & David E. Keyes & Marc G. Genton & Ying Sun, 2023. "Large‐scale environmental data science with ExaGeoStatR," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    13. Huang Huang & Sameh Abdulah & Ying Sun & Hatem Ltaief & David E. Keyes & Marc G. Genton, 2021. "Competition on Spatial Statistics for Large Datasets," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(4), pages 580-595, December.
    14. Morales-Oñate, Víctor & Crudu, Federico & Bevilacqua, Moreno, 2021. "Blockwise Euclidean likelihood for spatio-temporal covariance models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 176-201.
    15. Chen, Yewen & Chang, Xiaohui & Luo, Fangzhi & Huang, Hui, 2023. "Additive dynamic models for correcting numerical model outputs," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    16. Paciorek, Christopher J. & Lipshitz, Benjamin & Zhuo, Wei & Prabhat, . & Kaufman, Cari G. G. & Thomas, Rollin C., 2015. "Parallelizing Gaussian Process Calculations in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i10).
    17. Edwards, Matthew & Castruccio, Stefano & Hammerling, Dorit, 2020. "Marginally parameterized spatio-temporal models and stepwise maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    18. Karl Pazdernik & Ranjan Maitra & Douglas Nychka & Stephan Sain, 2018. "Reduced Basis Kriging for Big Spatial Fields," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 280-300, August.
    19. Ranadeep Daw & Christopher K. Wikle, 2023. "REDS: Random ensemble deep spatial prediction," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    20. Isabelle Grenier & Bruno Sansó & Jessica L. Matthews, 2024. "Multivariate nearest‐neighbors Gaussian processes with random covariance matrices," Environmetrics, John Wiley & Sons, Ltd., vol. 35(3), May.

    More about this item

    Statistics

    Access and download statistics

    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:wly:envmet:v:35:y:2024:i:4:n:e2844. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/1180-4009/ .

    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.