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Bayesian factor analysis with fat-tailed factors and its exact marginal likelihood. (English) Zbl 1163.62044
Summary: 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.
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.

##### MSC:
 62H25 Factor analysis and principal components; correspondence analysis 62F15 Bayesian inference 65C60 Computational problems in statistics (MSC2010) 65C05 Monte Carlo methods
tsbridge
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