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On Bayesian inference for generalized multivariate gamma distribution

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  • Das, Sourish
  • Dey, Dipak K.

Abstract

In this paper we define a generalized multivariate gamma (MG) distribution and develop various properties of this distribution. Then we consider a Bayesian decision theoretic approach to develop the inference technique for the related scale matrix [Sigma]. We show that maximum posteriori (MAP) estimate is a Bayes estimator. We also develop the testing problem for [Sigma] using a Bayes factor. This approach provides a mathematically closed form solution for [Sigma]. The only other approach to Bayesian inference for the MG distribution is given in Tsionas (2004), which is based on Markov Chain Monte Carlo (MCMC) technique. The Tsionas (2004) technique involves a costly matrix inversion whose computational complexity increases in cubic order, hence making inference infeasible for [Sigma], for large dimensions. In this paper, we provide an elegant closed form Bayes factor for [Sigma].

Suggested Citation

  • Das, Sourish & Dey, Dipak K., 2010. "On Bayesian inference for generalized multivariate gamma distribution," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1492-1499, October.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:19-20:p:1492-1499
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    References listed on IDEAS

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    1. Griffiths, R. C., 1984. "Characterization of infinitely divisible multivariate gamma distributions," Journal of Multivariate Analysis, Elsevier, vol. 15(1), pages 13-20, August.
    2. Mathai, A. M. & Moschopoulos, P. G., 1991. "On a multivariate gamma," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 135-153, October.
    3. Coelho, Carlos A., 1998. "The Generalized Integer Gamma Distribution--A Basis for Distributions in Multivariate Statistics," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 86-102, January.
    4. A. Mathal & P. Moschopoulos, 1992. "A form of multivariate gamma distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(1), pages 97-106, March.
    5. Furman, Edward, 2008. "On a multivariate gamma distribution," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2353-2360, October.
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    Cited by:

    1. Sourish Das & Aritra Halder & Dipak K. Dey, 2017. "Regularizing Portfolio Risk Analysis: A Bayesian Approach," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 865-889, September.
    2. Rajiv Sambasivan & Sourish Das & Sujit K. Sahu, 2020. "A Bayesian perspective of statistical machine learning for big data," Computational Statistics, Springer, vol. 35(3), pages 893-930, September.
    3. Kozubowski, Tomasz J. & Mazur, Stepan & Podgórski, Krzysztof, 2022. "Matrix Gamma Distributions and Related Stochastic Processes," Working Papers 2022:12, Örebro University, School of Business.
    4. Sourish Das, 2018. "Modeling Nelson-Siegel Yield Curve using Bayesian Approach," Papers 1809.06077, arXiv.org, revised Oct 2018.

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