IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v51y2024i3p1061-1085.html
   My bibliography  Save this article

G‐optimal grid designs for kriging models

Author

Listed:
  • Subhadra Dasgupta
  • Siuli Mukhopadhyay
  • Jonathan Keith

Abstract

This work is focused on finding G‐optimal designs theoretically for kriging models with two‐dimensional inputs and separable exponential covariance structures. For design comparison, the notion of evenness of two‐dimensional grid designs is developed. The mathematical relationship between the design and the supremum of the mean squared prediction error (SMSPE) function is studied and then optimal designs are explored for both prospective and retrospective design scenarios. In the case of prospective designs, the new design is developed before the experiment is conducted and the regularly spaced grid is shown to be the G‐optimal design. Retrospective designs are constructed by adding or deleting points from an already existing design. Deterministic algorithms are developed to find the best possible retrospective designs (which minimizes the SMSPE). It is found that a more evenly spread design under the G‐optimality criterion leads to the best possible retrospective design. For all the cases of finding the optimal prospective designs and the best possible retrospective designs, both frequentist and Bayesian frameworks have been considered. The proposed methodology for finding retrospective designs is illustrated with a spatiotemporal river water quality monitoring experiment.

Suggested Citation

  • Subhadra Dasgupta & Siuli Mukhopadhyay & Jonathan Keith, 2024. "G‐optimal grid designs for kriging models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1061-1085, September.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:3:p:1061-1085
    DOI: 10.1111/sjos.12699
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12699
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12699?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. Elizabeth G. Ryan & Christopher C. Drovandi & James M. McGree & Anthony N. Pettitt, 2016. "A Review of Modern Computational Algorithms for Bayesian Optimal Design," International Statistical Review, International Statistical Institute, vol. 84(1), pages 128-154, April.
    2. Nedka Dechkova Nikiforova & Rossella Berni & Gabriele Arcidiacono & Luciano Cantone & Pierpaolo Placidoli, 2021. "Latin hypercube designs based on strong orthogonal arrays and Kriging modelling to improve the payload distribution of trains," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(3), pages 498-516, February.
    3. Kinga Sikolya & Sándor Baran, 2020. "On the optimal designs for the prediction of complex Ornstein-Uhlenbeck processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(20), pages 4859-4870, October.
    4. Singh, Rakhi & Mukhopadhyay, Siuli, 2019. "Exact Bayesian designs for count time series," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 157-170.
    5. Singh, Satya Prakash & Mukhopadhyay, Siuli, 2016. "Bayesian crossover designs for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 35-50.
    6. Maroussa Zagoraiou & Alessandro Baldi Antognini, 2009. "Optimal designs for parameter estimation of the Ornstein–Uhlenbeck process," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(5), pages 583-600, September.
    7. 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, March.
    8. Yuanzhen He & Boxin Tang, 2013. "Strong orthogonal arrays and associated Latin hypercubes for computer experiments," Biometrika, Biometrika Trust, vol. 100(1), pages 254-260.
    9. Dette, Holger & Sperlich, Stefan, 1996. "Some applications of Stieltjes transforms in the construction of optimal designs for nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 21(3), pages 273-292, March.
    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. Jacopo Paglia & Jo Eidsvik & Juha Karvanen, 2022. "Efficient spatial designs using Hausdorff distances and Bayesian optimization," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1060-1084, September.
    2. K. Shuvo Bakar & Nicholas Biddle & Philip Kokic & Huidong Jin, 2020. "A Bayesian spatial categorical model for prediction to overlapping geographical areas in sample surveys," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 535-563, February.
    3. David J Price & Alexandre Breuzé & Richard Dybowski & Piero Mastroeni & Olivier Restif, 2017. "An efficient moments-based inference method for within-host bacterial infection dynamics," PLOS Computational Biology, Public Library of Science, vol. 13(11), pages 1-27, November.
    4. Victor De Oliveira & Zifei Han, 2022. "On Information About Covariance Parameters in Gaussian Matérn Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 690-712, December.
    5. Ng'ombe, John, 2019. "Economics of the Greenseeder Hand Planter, Discrete Choice Modeling, and On-Farm Field Experimentation," Thesis Commons jckt7, Center for Open Science.
    6. Song-Nan Liu & Min-Qian Liu & Jin-Yu Yang, 2023. "Construction of Column-Orthogonal Designs with Two-Dimensional Stratifications," Mathematics, MDPI, vol. 11(6), pages 1-27, March.
    7. Anyosa, Susan & Eidsvik, Jo & Pizarro, Oscar, 2023. "Adaptive spatial designs minimizing the integrated Bernoulli variance in spatial logistic regression models - with an application to benthic habitat mapping," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    8. Erum Zahid & Ijaz Hussain & Gunter Spöck & Muhammad Faisal & Javid Shabbir & Nasser M. AbdEl-Salam & Tajammal Hussain, 2016. "Spatial Prediction and Optimized Sampling Design for Sodium Concentration in Groundwater," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-16, September.
    9. Jiang, Bochuan & Wang, Zuzheng & Wang, Yaping, 2021. "Strong orthogonal arrays of strength two-plus based on the Addelman–Kempthorne method," Statistics & Probability Letters, Elsevier, vol. 175(C).
    10. 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.
    11. Dehideniya, Mahasen B. & Drovandi, Christopher C. & McGree, James M., 2018. "Optimal Bayesian design for discriminating between models with intractable likelihoods in epidemiology," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 277-297.
    12. Borgoni, Riccardo & Radaelli, Luigi & Tritto, Valeria & Zappa, Diego, 2013. "Optimal reduction of a spatial monitoring grid: Proposals and applications in process control," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 407-419.
    13. Joel A Paulson & Marc Martin-Casas & Ali Mesbah, 2019. "Fast uncertainty quantification for dynamic flux balance analysis using non-smooth polynomial chaos expansions," PLOS Computational Biology, Public Library of Science, vol. 15(8), pages 1-35, August.
    14. Wenlong Li & Min-Qian Liu & Jian-Feng Yang, 2022. "Construction of column-orthogonal strong orthogonal arrays," Statistical Papers, Springer, vol. 63(2), pages 515-530, April.
    15. 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.
    16. Letícia Ellen Dal Canton & Luciana Pagliosa Carvalho Guedes & Miguel Angel Uribe-Opazo, 2021. "Reduction of Sample Size in the Soil Physical-Chemical Attributes Using the Multivariate Effective Sample Size," Journal of Agricultural Studies, Macrothink Institute, vol. 9(1), pages 357-376, June.
    17. Granig, Wolfgang & Faller, Lisa-Marie & Hammerschmidt, Dirk & Zangl, Hubert, 2019. "Dependability considerations of redundant sensor systems," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    18. 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.
    19. Brendan Kochunas & Xun Huan, 2021. "Digital Twin Concepts with Uncertainty for Nuclear Power Applications," Energies, MDPI, vol. 14(14), pages 1-32, July.
    20. 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.

    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:bla:scjsta:v:51:y:2024:i:3:p:1061-1085. 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.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.