IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v31y2022i3d10.1007_s11749-022-00804-3.html
   My bibliography  Save this article

Some results on the Gaussian Markov Random Field construction problem based on the use of invariant subgraphs

Author

Listed:
  • Juan Baz

    (University of Oviedo)

  • Irene Díaz

    (University of Oviedo)

  • Susana Montes

    (University of Oviedo)

  • Raúl Pérez-Fernández

    (University of Oviedo)

Abstract

The study of Gaussian Markov Random Fields has attracted the attention of a large number of scientific areas due to its increasing usage in several fields of application. Here, we consider the construction of Gaussian Markov Random Fields from a graph and a positive-definite matrix, which is closely related to the problem of finding the Maximum Likelihood Estimator of the covariance matrix of the underlying distribution. In particular, it is simultaneously required that the variances and the covariances between variables associated with adjacent nodes in the graph are fixed by the positive-definite matrix and that pairs of variables associated with non-adjacent nodes in the graph are conditionally independent given all other variables. The solution to this construction problem exists and is unique up to the choice of a vector of means. In this paper, some results focusing on a certain type of subgraphs (invariant subgraphs) and a representation of the Gaussian Markov Random Field as a Multivariate Gaussian Markov Random Field are presented. These results ease the computation of the solution to the aforementioned construction problem.

Suggested Citation

  • Juan Baz & Irene Díaz & Susana Montes & Raúl Pérez-Fernández, 2022. "Some results on the Gaussian Markov Random Field construction problem based on the use of invariant subgraphs," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 856-874, September.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:3:d:10.1007_s11749-022-00804-3
    DOI: 10.1007/s11749-022-00804-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-022-00804-3
    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/s11749-022-00804-3?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. Ying C. MacNab, 2018. "Some recent work on multivariate Gaussian Markov random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 497-541, September.
    2. Nanny Wermuth & Eberhard Scheidt, 1977. "Fitting a Covariance Selection Model to a Matrix," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 88-92, March.
    3. Ying C. MacNab, 2018. "Rejoinder on: Some recent work on multivariate Gaussian Markov random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 554-569, September.
    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. Hentschel, Manuel & Engelke, Sebastian & Segers, Johan, 2022. "Statistical Inference for Hüsler–Reiss Graphical Models Through Matrix Completions," LIDAM Discussion Papers ISBA 2022032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Liangkun Fang & Zhangjie Wu & Yuan Tao & Jinfeng Gao, 2023. "Light Pollution Index System Model Based on Markov Random Field," Mathematics, MDPI, vol. 11(13), pages 1-18, July.

    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. F. Corpas-Burgos & P. Botella-Rocamora & M. A. Martinez-Beneito, 2019. "On the convenience of heteroscedasticity in highly multivariate disease mapping," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1229-1250, December.
    2. Sudipto Banerjee, 2023. "Discussion of “Optimal test procedures for multiple hypotheses controlling the familywise expected loss” by Willi Maurer, Frank Bretz, and Xiaolei Xun," Biometrics, The International Biometric Society, vol. 79(4), pages 2798-2801, December.
    3. Marcos O. Prates & Douglas R. M. Azevedo & Ying C. MacNab & Michael R. Willig, 2022. "Non‐separable spatio‐temporal models via transformed multivariate Gaussian Markov random fields," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1116-1136, November.
    4. Bhattacharya, Bhaskar, 2012. "Covariance selection and multivariate dependence," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 212-228.
    5. Miyamura, Masashi & Kano, Yutaka, 2006. "Robust Gaussian graphical modeling," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1525-1550, August.

    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:testjl:v:31:y:2022:i:3:d:10.1007_s11749-022-00804-3. 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.