Fitting the independent factor analysis model using the MCMC algorithm

Abstract

Independent factor analysis is a recent and novel latent variable model, in which the factors are supposed to be mutually independent and not necessarily Gaussian distributed. The factors are modeled by Gaussian mixtures that are quite flexible to approximate any probability density function. The model estimation can be quite promisingly solved by the EM algorithm when the number of factors is not too high. However, the computational burden needed to fit the model grows rapidly with the number of factors and the number of terms in the mixture involved. In any but the simplest cases, other estimation procedures have to be employed. In this work, an MCMC approach, based on the Gibbs sampler algorithm, is proposed. Its estimation performances are compared with the ordinary EM algorithm on real and simulated data.

Keywords:

• Mixture models
• Gibbs sampler
• EM algorithm

Acknowledgements

I am greatly indebted to Professor Jon Martin for retranscribing and posting me the data for the Chironomus larvae from the 1971 Atchley and Martin 9 paper upon which the second example is based. Further, I am really grateful to Professor Angela Montanari for reading and offering criticisms of the manuscript.

Additional information

Notes on contributors

Cinzia Viroli

Email: [email protected]