IDEAS home Printed from https://ideas.repec.org/a/spr/jclass/v35y2018i3d10.1007_s00357-018-9269-7.html
   My bibliography  Save this article

Risks of Classification of the Gaussian Markov Random Field Observations

Author

Listed:
  • Kęstutis Dučinskas

    (Klaipėda University
    Vilnius University)

  • Lina Dreižienė

    (Klaipėda University
    Vilnius University)

Abstract

Given the spatial lattice endowed with particular neighborhood structure, the problem of classifying a scalar Gaussian Markov random field (GMRF) observation into one of two populations specified by different regression coefficients and special parametric covariance (precision) matrix is considered. Classification rule based on the plug-in Bayes discriminant function with inserted ML estimators of regression coefficients, spatial dependence and scale parameters is studied. The novel closed-form expression for the actual risk and the approximation of the expected risk (AER) associated with the aforementioned classifier are derived. This is the extension of the previous study of GMRF classification to the case of complete parametric uncertainty. Derived AER is used as the main performance measure for the considered classifier. GMRF sampled on a regular 2-dimensional unit spacing lattice endowed with neighborhood structure based on the Euclidean distance between sites is used for a simulation experiment. The sampling properties of ML estimators and the accuracy of the derived AER for various values of spatial dependence parameters and Mahalanobis distance are studied. The influence of the neighborhood size on the accuracy of the proposed AER is examined as well.

Suggested Citation

  • Kęstutis Dučinskas & Lina Dreižienė, 2018. "Risks of Classification of the Gaussian Markov Random Field Observations," Journal of Classification, Springer;The Classification Society, vol. 35(3), pages 422-436, October.
    • Handle: RePEc:spr:jclass:v:35:y:2018:i:3:d:10.1007_s00357-018-9269-7
    DOI: 10.1007/s00357-018-9269-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00357-018-9269-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00357-018-9269-7?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
    ---><---

    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. Markus Abt, 1999. "Estimating the Prediction Mean Squared Error in Gaussian Stochastic Processes with Exponential Correlation Structure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(4), pages 563-578, December.
    2. Victor De Oliveira & Marco Ferreira, 2011. "Maximum likelihood and restricted maximum likelihood estimation for a class of Gaussian Markov random fields," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 167-183, September.
    3. Dale Zimmerman & Noel Cressie, 1992. "Mean squared prediction error in the spatial linear model with estimated covariance parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(1), pages 27-43, March.
    4. A. Batsidis & K. Zografos, 2011. "Errors of misclassification in discrimination of dimensional coherent elliptic random field observations," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(4), pages 446-461, November.
    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. Dučinskas, Kęstutis & Dreižienė, Lina & Zikarienė, Eglė, 2015. "Multiclass classification of the scalar Gaussian random field observation with known spatial correlation function," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 107-114.
    2. Li, Mengyuan & Yu, Dalei & Bai, Peng, 2013. "A note on the existence and uniqueness of quasi-maximum likelihood estimators for mixed regressive, spatial autoregression models," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 568-572.
    3. Ferreira, Marco A.R. & Porter, Erica M. & Franck, Christopher T., 2021. "Fast and scalable computations for Gaussian hierarchical models with intrinsic conditional autoregressive spatial random effects," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    4. Kleijnen, Jack P.C. & van Beers, W.C.M. & van Nieuwenhuyse, I., 2011. "Expected Improvement in Efficient Global Optimization Through Bootstrapped Kriging - Replaces CentER DP 2010-62," Discussion Paper 2011-015, Tilburg University, Center for Economic Research.
    5. C. Helbert & D. Dupuy & L. Carraro, 2009. "Assessment of uncertainty in computer experiments from Universal to Bayesian Kriging," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(2), pages 99-113, March.
    6. Lisa Henn & James S. Hodges, 2014. "Multiple Local Maxima in Restricted Likelihoods and Posterior Distributions for Mixed Linear Models," International Statistical Review, International Statistical Institute, vol. 82(1), pages 90-105, April.
    7. David Ginsbourger & Delphine Dupuy & Anca Badea & Laurent Carraro & Olivier Roustant, 2009. "A note on the choice and the estimation of Kriging models for the analysis of deterministic computer experiments," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(2), pages 115-131, March.
    8. Monica Pratesi & Nicola Salvati, 2008. "Small area estimation: the EBLUP estimator based on spatially correlated random area effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(1), pages 113-141, February.
    9. Iranpanah, N. & Mohammadzadeh, M. & Taylor, C.C., 2011. "A comparison of block and semi-parametric bootstrap methods for variance estimation in spatial statistics," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 578-587, January.
    10. William F. Christensen, 2011. "Filtered Kriging for Spatial Data with Heterogeneous Measurement Error Variances," Biometrics, The International Biometric Society, vol. 67(3), pages 947-957, September.
    11. Werner Müller & Milan Stehlík, 2009. "Issues in the optimal design of computer simulation experiments," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(2), pages 163-177, March.
    12. Bachoc, François, 2014. "Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 1-35.
    13. Huang, Whitney K. & Chung, Yu-Min & Wang, Yu-Bo & Mandel, Jeff E. & Wu, Hau-Tieng, 2022. "Airflow recovery from thoracic and abdominal movements using synchrosqueezing transform and locally stationary Gaussian process regression," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    14. Jack Kleijnen & Wim Beers & Inneke Nieuwenhuyse, 2012. "Expected improvement in efficient global optimization through bootstrapped kriging," Journal of Global Optimization, Springer, vol. 54(1), pages 59-73, 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:spr:jclass:v:35:y:2018:i:3:d:10.1007_s00357-018-9269-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.