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Bayesian analysis of matrix normal graphical models

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  • Hao Wang
  • Mike West

Abstract

We present Bayesian analyses of matrix-variate normal data with conditional independencies induced by graphical model structuring of the characterizing covariance matrix parameters. This framework of matrix normal graphical models includes prior specifications, posterior computation using Markov chain Monte Carlo methods, evaluation of graphical model uncertainty and model structure search. Extensions to matrix-variate time series embed matrix normal graphs in dynamic models. Examples highlight questions of graphical model uncertainty, search and comparison in matrix data contexts. These models may be applied in a number of areas of multivariate analysis, time series and also spatial modelling. Copyright 2009, Oxford University Press.

Suggested Citation

  • Hao Wang & Mike West, 2009. "Bayesian analysis of matrix normal graphical models," Biometrika, Biometrika Trust, vol. 96(4), pages 821-834.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:4:p:821-834
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    File URL: http://hdl.handle.net/10.1093/biomet/asp049
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    Cited by:

    1. Gruber, Lutz F. & West, Mike, 2017. "Bayesian online variable selection and scalable multivariate volatility forecasting in simultaneous graphical dynamic linear models," Econometrics and Statistics, Elsevier, vol. 3(C), pages 3-22.
    2. Billio, Monica & Casarin, Roberto & Costola, Michele & Iacopini, Matteo, 2024. "COVID-19 spreading in financial networks: A semiparametric matrix regression model," Econometrics and Statistics, Elsevier, vol. 29(C), pages 113-131.
    3. Joshua Chan & Arnaud Doucet & Roberto León-González & Rodney W. Strachan, 2018. "Multivariate stochastic volatility with co-heteroscedasticity," CAMA Working Papers 2018-52, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    4. Roberto Casarin, 2014. "A Note on Tractable State-Space Model for Symmetric Positive-Definite Matrices," Working Papers 2014:23, Department of Economics, University of Venice "Ca' Foscari".
    5. Ruey S. Tsay, 2024. "Matrix‐Variate Time Series Analysis: A Brief Review and Some New Developments," International Statistical Review, International Statistical Institute, vol. 92(2), pages 246-262, August.
    6. Bianchi, Daniele & Billio, Monica & Casarin, Roberto & Guidolin, Massimo, 2019. "Modeling systemic risk with Markov Switching Graphical SUR models," Journal of Econometrics, Elsevier, vol. 210(1), pages 58-74.
    7. Seongoh Park & Johan Lim & Xinlei Wang & Sanghan Lee, 2019. "Permutation based testing on covariance separability," Computational Statistics, Springer, vol. 34(2), pages 865-883, June.
    8. Yin, Jianxin & Li, Hongzhe, 2012. "Model selection and estimation in the matrix normal graphical model," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 119-140.
    9. Jouchi Nakajima & Mike West, 2013. "Bayesian Analysis of Latent Threshold Dynamic Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(2), pages 151-164, April.
    10. Bekker, Andriëtte & van Niekerk, Janet & Arashi, Mohammad, 2017. "Wishart distributions: Advances in theory with Bayesian application," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 272-283.
    11. Suprateek Kundu & Benjamin B. Risk, 2021. "Scalable Bayesian matrix normal graphical models for brain functional networks," Biometrics, The International Biometric Society, vol. 77(2), pages 439-450, June.
    12. Mike West, 2020. "Bayesian forecasting of multivariate time series: scalability, structure uncertainty and decisions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 1-31, February.
    13. Yang Ni & Peter Müller & Yitan Zhu & Yuan Ji, 2018. "Heterogeneous reciprocal graphical models," Biometrics, The International Biometric Society, vol. 74(2), pages 606-615, June.
    14. Dipankar Bandyopadhyay & Antonio Canale, 2016. "Non-parametric spatial models for clustered ordered periodontal data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(4), pages 619-640, August.
    15. Wang, Hao, 2010. "Sparse seemingly unrelated regression modelling: Applications in finance and econometrics," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2866-2877, November.
    16. Monica Billio & Roberto Casarin & Matteo Iacopini & Sylvia Kaufmann, 2023. "Bayesian Dynamic Tensor Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(2), pages 429-439, April.
    17. Beatrice Franzolini & Alexandros Beskos & Maria De Iorio & Warrick Poklewski Koziell & Karolina Grzeszkiewicz, 2022. "Change point detection in dynamic Gaussian graphical models: the impact of COVID-19 pandemic on the US stock market," Papers 2208.00952, arXiv.org, revised May 2023.
    18. Zhou, Xiaocong & Nakajima, Jouchi & West, Mike, 2014. "Bayesian forecasting and portfolio decisions using dynamic dependent sparse factor models," International Journal of Forecasting, Elsevier, vol. 30(4), pages 963-980.
    19. Fangting Zhou & Kejun He & Kunbo Wang & Yanxun Xu & Yang Ni, 2023. "Functional Bayesian networks for discovering causality from multivariate functional data," Biometrics, The International Biometric Society, vol. 79(4), pages 3279-3293, December.
    20. Viroli, Cinzia, 2012. "On matrix-variate regression analysis," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 296-309.

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