Papers on Bayesian factor analysis? I am interested in fitting a factor analysis-like model on asset returns or other similar latent variable models. What are good papers to read on this topic? I am particularly interested in how to handle the fact that a factor analysis model is identical under a sign change for the "factor loadings".
 A: Some references to help you out. 


*

*Tipping, M. E. & Bishop, C. M.
Probabilistic principal component
analysis Journal of the Royal
Statistical Society (Series B),
1999, 21, 611-622

*Tom Minka. Automatic choice of
dimensionality for PCA. NIPS 2000
url:
http://research.microsoft.com/en-us/um/people/minka/papers/pca/

*Šmídl, V. & Quinn, A. On Bayesian
principal component analysis
Computational Statistics & Data
Analysis, 2007, 51, 4101-4123


If you are familiar with information theoretic model selection (MML, MDL, etc.), I highly recommend checking out:


*

*Wallace, C. S. & Freeman, P. R.
Single-Factor Analysis by Minimum
Message Length Estimation Journal of
the Royal Statistical Society
(Series B), 1992, 54, 195-209

*C. S. Wallace. Multiple Factor
Analysis by MML Estimation.
http://www.allisons.org/ll/Images/People/Wallace/Multi-Factor/
Tech report:
http://www.allisons.org/ll/Images/People/Wallace/Multi-Factor/TR95.218.pdf
A: Here are a few suggestions, more from the statistics literature, with an eye toward applications in finance:

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*Geweke, J., & Zhou, G. (1996). Measuring the pricing error of the arbitrage pricing theory. Review of Financial Studies, 9(2), 557. Soc Financial Studies. Retrieved January 29, 2011, from http://rfs.oxfordjournals.org/content/9/2/557.abstract.

You might start here - a detailed discussion of identifiability issues (related to and including the sign indeterminacy you describe)


*Aguilar, O., & West, M. (2000). Bayesian Dynamic Factor Models and Portfolio Allocation. Journal of Business & Economic Statistics, 18(3), 338. doi: 10.2307/1392266.


*Lopes, H. F., & West, M. (2004). Bayesian model assessment in factor analysis. Statistica Sinica, 14(1), 41â68. Citeseer. Retrieved September 19, 2010, from here.
Good luck!
A: You should take a look at some of the nonparametric Bayesian approaches (see this paper and this paper) to factor analysis which do not assume the number of factors to be known; the first one can also model the case where the factors have a dependency structure among them.
A: A decent overview of factor analysis is Latent Variable Methods and Factor Analysis by Bartholomew and Knott. They write about the interpretation of latent factors. This book is not as algorithmically-oriented as I would like, but their description of e.g. partial factor analysis is decent.
A: This article deals with Bayesian estimation of dynamical hierarchical factor model:
E. Moench, S. Ng, S. Potter. Dynamic Hierarchical Factor Models, Federal Reserve Bank of New York, 2009, Report No. 412. link.
Naturally it can be adapted for non-hierarchical case. As usual you will find more references on topic by perusing the references in the article.
