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

Journal of Multivariate Analysis

Volumn 100, Issue 8, 2009, Pages 1717-1726

  Ando, Tomohiro ^a  

^a KEIO UNIVERSITY   (Japan)

Author keywords

Bayesian methods; Marginal likelihood; Matrix variate t distribution; Model selection

Indexed keywords

EID: 67349234862     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2009.02.001     Document Type: Article

References (46)

1. Aguilar O., and West M. Bayesian dynamic factor models and variance matrix discounting for portfolio allocation. J. Bus. Econom. Statist. 18 (2000) 338-357
2. Lopes H.F., and West M. Bayesian model assessment in factor analysis. Statist. Sinica 14 (2004) 41-67
3. Press S.J., and Shigemasu K. Bayesian inference in factor analysis. In: Gleser L., Perleman M., Press S.J., and Sampson A. (Eds). Contributions to Probability and Statistics (1989), Springer-Verlag, New York 271-287
4. West M. Bayesian factor regression models in the "large p, small n" paradigm. In: Bernardo J.M., Bayarri M.J., Berger J.O., Dawid A.P., Heckerman D., Smith A.F.M., and West M. (Eds). Bayesian Statistics vol. 7 (2003), Oxford University Press, Oxford 723-732
5. Kass R., and Raftery A. Bayes factors. J. Amer. Statist. Assoc. 90 (1995) 773-795
6. Press S.J., and Shigemasu K. A note on choosing the number of factors. Comm. Statist. Theory Methods 28 (1999) 1653-1670
7. Schwarz G. Estimating the dimension of a model. Ann. Statist. 6 (1978) 461-464
8. Konishi S., Ando T., and Imoto S. Bayesian information criteria and smoothing parameter selection in radial basis function networks. Biometrika 91 (2004) 27-43
9. Berger J.O., Ghosh J.K., and Mukhopadhyay N. Approximation and consistency of Bayes factors as model dimension grows. J. Statist. Plann. Inference 112 (2003) 241-258
10. Lee S.Y., and Song X.Y. Bayesian selection on the number of factors in a factor analysis model. Behaviormetrika 29 (2002) 23-39
11. Press S.J. Subjective and Objective Bayesian Statistics. Principles Models and Applications (2003), Wiley, New Jersey
12. Chib S. Marginal likelihood from the Gibbs output. J. Amer. Statist. Assoc. 90 (1995) 1313-1321
13. Newton M.A., and Raftery A.E. Approximate Bayesian inference with the weighted likelihood bootstrap. J. Roy. Stat. Soc. Ser. B 56 (1994) 3-48
14. Gelfand A.E., and Dey D. Bayesian model choice: Asymptotics and exact calculations. J. Roy. Stat. Soc. Ser. B 56 (1994) 501-514
15. Lewis S.M., and Raftery A.E. Estimating Bayes factors via posterior simulation with the Laplace-Metropolis estimator. J. Amer. Statist. Assoc. 92 (1997) 648-655
16. Meng X.L., and Wong W.H. Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. Statist. Sinica 6 (1996) 831-860
17. Green P. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 (1995) 711-732
18. Tucker L.R. The role of correlated factors in factor analysis. Psychometrika 5 (1940) 141-152
19. Lee S.Y., and Xia Y.M. Maximum likelihood methods in treating outliers and symmetrically heavy-tailed distributions for nonlinear structural equation models with missing data. Psychometrika 71 (2006) 565-585
20. Lee S.Y., and Xia Y.M. A robust Bayesian approach for structural equation models with missing data. Psychometrika 73 (2008) 343-364
21. Lee S.Y., and Xia Y.M. Semiparametric Bayesian analysis of structural equation models with fixed covariates. Statist. Med. 27 (2008) 2341-2360
22. Geweke J.F. Contemporary Bayesian Econometrics and Statistics (2005), Wiley, New York
23. Lawley D.N. The estimation of factor loadings by the method of maximum likelihood. Proc. Roy. Soc. Edinburgh Ser. A 60 (1940) 64-82
24. Seber G.A.F. Multivariate Observations (1984), Wiley, New York
25. Geweke J.F., and Singleton K.J. Interpreting the likelihood ratio statistic in factor models when sample size is small. J. Amer. Statist. Assoc. 75 (1980) 133-137
26. Geweke J.F., and Zhou G. Measuring the pricing error of the arbitrage pricing theory. Rev. Finan. Stud. 9 (1996) 557-587
27. Yalcin I., and Amemiya Y. Nonlinear factor analysis as a statistical method. Statist. Sci. 16 (2001) 275-294
28. Lewin-Koh S.C., and Amemiya Y. Heteroscedastic factor analysis. Biometrika 90 (2003) 85-97
29. D.B. Rowe, Correlated Bayesian factor analysis, Ph.D. Thesis, Department of Statistics, University of California, Riverside, 1998
30. Dickey J.M. Matricvariate generalizations of the multivariate t-distribution and the inverted multivariate t-distribution. Ann. Math. Statist. 38 (1967) 511-518
31. Javier W.R., and Gupta A.K. On matric variate-t distribution. Comm. Statist. Theory Methods 14 (1985) 1413-1425
32. Phillips P.C.B. The distribution of matrix quotients. J. Multivariate Anal. 16 (1985) 157-161
33. Lee S.Y. Structural Equation Modelling: A Bayesian Approach (2007), John Wiley and Sons, England
34. Ando T. Bayesian inference for nonlinear and non-Gaussian stochastic volatility model with leverage effect. J. Japan Statist. Soc. 36 (2006) 173-197
35. Ando T. Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models. Biometrika 94 (2007) 443-458
36. Ando T. Bayesian model averaging and Bayesian predictive information criterion for model selection. J. Japan Statist. Soc. 38 (2008) 243-257
37. Ando T., Konishi S., and Imoto S. Nonlinear regression modeling via regularized radial basis function networks. J. Statist. Plann. Inference 138 (2008) 3616-3633
38. T. Ando, S. Konishi, Nonlinear logistic discrimination via regularized radial basis functions for classifying high-dimensional data, Ann. Inst. Statist. Math. (2007) (in press)
39. Zellner A. An Introduction to Bayesian Inference in Econometrics (1971), John Wiley and Sons, New York
40. Konishi S., and Kitagawa G. Generalised information criteria in model selection. Biometrika 83 (1996) 875-890
41. Gelfand A.E., Dey D., and Chang H. Model determination using predictive distributions with implementation via sampling-based methods (with discussion). In: Bernardo J.M., Berger J.O., Dawid A.P., and Smith A.F.M. (Eds). Bayesian Statistics vol. 4 (1992), Oxford University Press, Oxford 147-167
42. Rossi P., Gilula Z., and Allenby G. Overcoming scale usage heterogeneity: A Bayesian hierarchical approach. J. Amer. Statist. Assoc. 96 (2001) 20-31
43. Kendall M. Multivariate Analysis (1980), Charles Griffin and Company LTD., London
44. Bai J., and Ng S. Determining the number of factors in approximate factor models. Econometrica 70 (2002) 191-221
45. Akaike H. Factor analysis. AIC Psychometrika 3 (1987) 317-332
46. Bozdogan H. Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions. Psychometrika 52 (1987) 345-370