IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v78y2024i3p491-504.html

Scaling priors for intrinsic Gaussian Markov random fields applied to blood pressure data

Author

Listed:
  • Maria‐Zafeiria Spyropoulou
  • James Bentham

Abstract

An Intrinsic Gaussian Markov Random Field (IGMRF) can be used to induce conditional dependence in Bayesian hierarchical models. IGMRFs have both a precision matrix, which defines the neighborhood structure of the model, and a precision, or scaling, parameter. Previous studies have shown the importance of selecting the prior for this scaling parameter appropriately for different types of IGMRF, as it can have a substantial impact on posterior estimates. Here, we focus on cases in one and two dimensions, where tuning of the prior is achieved by mapping it to the marginal SD of an IGMRF of corresponding dimensionality. We compare the effects of scaling various IGMRFs, including an application to real two‐dimensional blood pressure data using MCMC methods.

Suggested Citation

  • Maria‐Zafeiria Spyropoulou & James Bentham, 2024. "Scaling priors for intrinsic Gaussian Markov random fields applied to blood pressure data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 78(3), pages 491-504, August.
    • Handle: RePEc:bla:stanee:v:78:y:2024:i:3:p:491-504
    DOI: 10.1111/stan.12330
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/stan.12330
    Download Restriction: no
    File URL: https://libkey.io/10.1111/stan.12330?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. Sigrunn H. Sørbye & Håvard Rue, 2011. "Simultaneous Credible Bands for Latent Gaussian Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(4), pages 712-725, December.
    2. Thon, Kevin & Rue, Håvard & Skrøvseth, Stein Olav & Godtliebsen, Fred, 2012. "Bayesian multiscale analysis of images modeled as Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 49-61, January.
    3. 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.
    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. Rajala, T. & Penttinen, A., 2014. "Bayesian analysis of a Gibbs hard-core point pattern model with varying repulsion range," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 530-541.
    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. Laura M. Sangalli, 2021. "Spatial Regression With Partial Differential Equation Regularisation," International Statistical Review, International Statistical Institute, vol. 89(3), pages 505-531, December.
    4. Stefano Castruccio & Joseph Guinness, 2017. "An evolutionary spectrum approach to incorporate large-scale geographical descriptors on global processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 329-344, February.
    5. 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.
    6. William Kleiber & Stephan Sain & Luke Madaus & Patrick Harr, 2023. "Stochastic tropical cyclone precipitation field generation," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    7. Korte-Stapff, Moritz & Karvonen, Toni & Moulines, Éric, 2025. "Smoothness estimation for Whittle–Matérn processes on closed Riemannian manifolds," Stochastic Processes and their Applications, Elsevier, vol. 189(C).
    8. Finn Lindgren, 2015. "Comments on: Comparing and selecting spatial predictors using local criteria," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 35-44, March.
    9. Carson, Stuart & Mills Flemming, Joanna, 2014. "Seal encounters at sea: A contemporary spatial approach using R-INLA," Ecological Modelling, Elsevier, vol. 291(C), pages 175-181.
    10. 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).
    11. 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).
    12. Kleiber, William & Nychka, Douglas, 2012. "Nonstationary modeling for multivariate spatial processes," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 76-91.
    13. Andre Python & Andreas Bender & Marta Blangiardo & Janine B. Illian & Ying Lin & Baoli Liu & Tim C.D. Lucas & Siwei Tan & Yingying Wen & Davit Svanidze & Jianwei Yin, 2022. "A downscaling approach to compare COVID‐19 count data from databases aggregated at different spatial scales," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(1), pages 202-218, January.
    14. Simon N. Wood, 2020. "Inference and computation with generalized additive models and their extensions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 307-339, June.
    15. Coll, M. & Pennino, M. Grazia & Steenbeek, J. & Sole, J. & Bellido, J.M., 2019. "Predicting marine species distributions: Complementarity of food-web and Bayesian hierarchical modelling approaches," Ecological Modelling, Elsevier, vol. 405(C), pages 86-101.
    16. 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.
    17. Ruiman Zhong & Paula Moraga, 2024. "Bayesian Hierarchical Models for the Combination of Spatially Misaligned Data: A Comparison of Melding and Downscaler Approaches Using INLA and SPDE," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(1), pages 110-129, March.
    18. Daniela Silva & Raquel Menezes & Ana Moreno & Ana Teles-Machado & Susana Garrido, 2024. "Environmental Effects on the Spatiotemporal Variability of Sardine Distribution Along the Portuguese Continental Coast," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(3), pages 553-575, September.
    19. Laura Serra & Claudio Detotto & Marco Vannini, 2022. "Public lands as a mitigator of wildfire burned area using a spatio-temporal model applied in Sardinia," Letters in Spatial and Resource Sciences, Springer, vol. 15(3), pages 621-635, December.
    20. Vanhatalo, Jarno & Veneranta, Lari & Hudd, Richard, 2012. "Species distribution modeling with Gaussian processes: A case study with the youngest stages of sea spawning whitefish (Coregonus lavaretus L. s.l.) larvae," Ecological Modelling, Elsevier, vol. 228(C), pages 49-58.

    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:stanee:v:78:y:2024:i:3:p:491-504. 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=0039-0402 .

    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.