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A skew Gaussian decomposable graphical model

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  • Zareifard, Hamid
  • Rue, Håvard
  • Khaledi, Majid Jafari
  • Lindgren, Finn

Abstract

This paper proposes a novel decomposable graphical model to accommodate skew Gaussian graphical models. We encode conditional independence structure among the components of the multivariate closed skew normal random vector by means of a decomposable graph so that the pattern of zero off-diagonal elements in the precision matrix corresponds to the missing edges of the given graph. We present conditions that guarantee the propriety of the posterior distributions under the standard noninformative priors for mean vector and precision matrix, and a proper prior for skewness parameter. The identifiability of the parameters is investigated by a simulation study. Finally, we apply our methodology to two data sets.

Suggested Citation

  • Zareifard, Hamid & Rue, Håvard & Khaledi, Majid Jafari & Lindgren, Finn, 2016. "A skew Gaussian decomposable graphical model," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 58-72.
    • Handle: RePEc:eee:jmvana:v:145:y:2016:i:c:p:58-72
    DOI: 10.1016/j.jmva.2015.08.011
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    References listed on IDEAS

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    1. Nakajima, Jouchi & Kasuya, Munehisa & Watanabe, Toshiaki, 2011. "Bayesian analysis of time-varying parameter vector autoregressive model for the Japanese economy and monetary policy," Journal of the Japanese and International Economies, Elsevier, vol. 25(3), pages 225-245, September.
    2. MOUCHART, Michel, 1976. "A note on Bayes theorem," LIDAM Reprints CORE 253, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    4. Zhengyuan Zhu & Yufeng Liu, 2009. "Estimating spatial covariance using penalised likelihood with weighted penalty," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(7), pages 925-942.
    5. A. Capitanio & A. Azzalini & E. Stanghellini, 2003. "Graphical models for skew‐normal variates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 129-144, March.
    6. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 821-852.
    7. Jouchi Nakajima & Toshiaki Watanabe, 2011. "Bayesian Analysis of Time-Varying Parameter Vector Autoregressive Model with the Ordering of Variables for the Japanese Economy and Monetary Policy," Global COE Hi-Stat Discussion Paper Series gd11-196, Institute of Economic Research, Hitotsubashi University.
    8. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
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    Cited by:

    1. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Linh H. Nghiem & Francis K. C. Hui & Samuel Müller & Alan H. Welsh, 2022. "Estimation of graphical models for skew continuous data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1811-1841, December.

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