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Simulation of hyper-inverse Wishart distributions in graphical models

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  • Carlos M. Carvalho
  • Hélène Massam
  • Mike West

Abstract

We introduce and exemplify an efficient method for direct sampling from hyper-inverse Wishart distributions. The method relies very naturally on the use of standard junction-tree representation of graphs, and couples these with matrix results for inverse Wishart distributions. We describe the theory and resulting computational algorithms for both decomposable and nondecomposable graphical models. An example drawn from financial time series demonstrates application in a context where inferences on a structured covariance model are required. We discuss and investigate questions of scalability of the simulation methods to higher-dimensional distributions. The paper concludes with general comments about the approach, including its use in connection with existing Markov chain Monte Carlo methods that deal with uncertainty about the graphical model structure. Copyright 2007, Oxford University Press.

Suggested Citation

  • Carlos M. Carvalho & Hélène Massam & Mike West, 2007. "Simulation of hyper-inverse Wishart distributions in graphical models," Biometrika, Biometrika Trust, vol. 94(3), pages 647-659.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:3:p:647-659
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    File URL: http://hdl.handle.net/10.1093/biomet/asm056
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    Cited by:

    1. 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.
    2. Billio, Monica & Casarin, Roberto & Rossini, Luca, 2019. "Bayesian nonparametric sparse VAR models," Journal of Econometrics, Elsevier, vol. 212(1), pages 97-115.
    3. Ahelegbey, Daniel Felix, 2015. "The Econometrics of Bayesian Graphical Models: A Review With Financial Application," MPRA Paper 92634, University Library of Munich, Germany, revised 25 Apr 2016.
    4. Collins, Benoît & Matsumoto, Sho & Saad, Nadia, 2014. "Integration of invariant matrices and moments of inverses of Ginibre and Wishart matrices," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 1-13.
    5. Paci, Lucia & Consonni, Guido, 2020. "Structural learning of contemporaneous dependencies in graphical VAR models," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    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. Nicola, Giancarlo & Cerchiello, Paola & Aste, Tomaso, 2020. "Information network modeling for U.S. banking systemic risk," LSE Research Online Documents on Economics 107563, London School of Economics and Political Science, LSE Library.
    8. 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.
    9. Liang, Ye & Sun, Dongchu, 2012. "Objective priors for generative star-shape models," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 991-997.
    10. 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.
    11. Daniel Felix Ahelegbey & Paolo Giudici, 2020. "Market Risk, Connectedness and Turbulence: A Comparison of 21st Century Financial Crises," DEM Working Papers Series 188, University of Pavia, Department of Economics and Management.
    12. 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.
    13. 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.
    14. Daniel Felix Ahelegbey, 2015. "The Econometrics of Networks: A Review," Working Papers 2015:13, Department of Economics, University of Venice "Ca' Foscari".

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