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Bayesian factor analysis with fat-tailed factors and its exact marginal likelihood


  • Ando, Tomohiro


The traditional Bayesian factor analysis method is extended. In contrast to the case for previous studies, the matrix variate t-distribution is utilized to provide a prior density on the latent factors. This is a natural extension of the traditional model and yields many advantages. The crucial issue is the selection of the number of factors. The marginal likelihood, constructed by asymptotic and computational approaches, is generally utilized for this problem. However, both theoretical and computational problems have arisen. In this paper, the exact marginal likelihood is derived. It enables us to evaluate posterior model probabilities without inducing the above problems. Monte Carlo experiments were conducted to examine the performance of the proposed Bayesian factor analysis modelling methodology. The simulation results show that the proposed methodology performs well.

Suggested Citation

  • Ando, Tomohiro, 2009. "Bayesian factor analysis with fat-tailed factors and its exact marginal likelihood," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1717-1726, September.
  • Handle: RePEc:eee:jmvana:v:100:y:2009:i:8:p:1717-1726

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    References listed on IDEAS

    1. Sik-Yum Lee & Ye-Mao Xia, 2006. "Maximum Likelihood Methods in Treating Outliers and Symmetrically Heavy-Tailed Distributions for Nonlinear Structural Equation Models with Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 565-585, September.
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    5. Geweke, John & Zhou, Guofu, 1996. "Measuring the Pricing Error of the Arbitrage Pricing Theory," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 557-587.
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    7. Ledyard Tucker, 1940. "The role of correlated factors in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 5(2), pages 141-152, June.
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    9. Phillips, P. C. B., 1985. "The distribution of matrix quotients," Journal of Multivariate Analysis, Elsevier, vol. 16(1), pages 157-161, February.
    10. Hirotugu Akaike, 1987. "Factor analysis and AIC," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 317-332, September.
    11. Sock-Cheng Lewin-Koh, 2003. "Heteroscedastic factor analysis," Biometrika, Biometrika Trust, vol. 90(1), pages 85-97, March.
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    Cited by:

    1. Tsay, Ruey S. & Ando, Tomohiro, 2012. "Bayesian panel data analysis for exploring the impact of subprime financial crisis on the US stock market," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3345-3365.
    2. Leung, Dennis & Drton, Mathias, 2016. "Order-invariant prior specification in Bayesian factor analysis," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 60-66.


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