Zhihua Zhang, Kap Luk Chan, James T. Kwok, and Dit-Yan Yeung
Based on the probabilistic reformulation of principal component analysis (PCA), we consider the problem of determining the number of principal components as a model selection problem. We present a hierarchical model for probabilistic PCA and construct a Bayesian inference method for this model using reversible jump Markov chain Monte Carlo (MCMC). By regarding each principal component as a point in a one-dimensional space and employing only birthdeath moves in our reversible jump methodology, our proposed method is simple and capable of automatically determining the number of principal components and estimating the parameters simultaneously under the same disciplined framework. Simulation experiments are performed to demonstrate the effectiveness of our MCMC method.