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Rejoinder on: Some recent work on multivariate Gaussian Markov random fields

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  • Ying C. MacNab

    (University of British Columbia)

Abstract

I thank the discussants, Miguel A. Martinez-Beneito, Fedel Greco, Carlo Trivisano, Stephan R Sain, and Reinhard Furrer, for their insightful and stimulating commentary. The rejoinder is organized in five sections: (1) the M-based models, (2) posterior sensitivity to prior choices for $${\varvec{C}}$$ C and $${\varvec{\varSigma }}$$ Σ , (3) stationary and non-stationary (M)GMRFs, (4) various approaches to model formulation and related applications, and (5) statistical computation.

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  • 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.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:3:d:10.1007_s11749-018-0608-0
    DOI: 10.1007/s11749-018-0608-0
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    References listed on IDEAS

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    1. Hååvard Rue & Hååkon Tjelmeland, 2002. "Fitting Gaussian Markov Random Fields to Gaussian Fields," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 31-49, March.
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    4. Miguel A. Martinez-Beneito, 2013. "A general modelling framework for multivariate disease mapping," Biometrika, Biometrika Trust, vol. 100(3), pages 539-553.
    5. Ying C. MacNab & Patrick J. Farrell & Paul Gustafson & Sijin Wen, 2004. "Estimation in Bayesian Disease Mapping," Biometrics, The International Biometric Society, vol. 60(4), pages 865-873, December.
    6. Zammit-Mangion, Andrew & Rougier, Jonathan, 2018. "A sparse linear algebra algorithm for fast computation of prediction variances with Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 116-130.
    7. Håvard Rue, 2001. "Fast sampling of Gaussian Markov random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 325-338.
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    12. Cressie, Noel & Verzelen, Nicolas, 2008. "Conditional-mean least-squares fitting of Gaussian Markov random fields to Gaussian fields," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2794-2807, January.
    13. 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.
    14. MacNab, Ying C. & Lin, Yi, 2009. "On empirical Bayes penalized quasi-likelihood inference in GLMMs and in Bayesian disease mapping and ecological modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2950-2967, June.
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    Cited by:

    1. 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.
    2. 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.
    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. 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.

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