Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1717-1726 |
| Number of pages | 10 |
| Journal | Journal of Multivariate Analysis |
| Volume | 100 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 2009 Sep |
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Keywords
- Bayesian methods
- Marginal likelihood
- Matrix variate t-distribution
- Model selection
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Numerical Analysis
- Statistics and Probability
Cite this
Bayesian factor analysis with fat-tailed factors and its exact marginal likelihood. / Ando, Tomohiro.
In: Journal of Multivariate Analysis, Vol. 100, No. 8, 09.2009, p. 1717-1726.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Bayesian factor analysis with fat-tailed factors and its exact marginal likelihood
AU - Ando, Tomohiro
PY - 2009/9
Y1 - 2009/9
N2 - 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.
AB - 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.
KW - Bayesian methods
KW - Marginal likelihood
KW - Matrix variate t-distribution
KW - Model selection
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UR - http://www.scopus.com/inward/citedby.url?scp=67349234862&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2009.02.001
DO - 10.1016/j.jmva.2009.02.001
M3 - Article
VL - 100
SP - 1717
EP - 1726
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
SN - 0047-259X
IS - 8
ER -