  Principal component analysis (PCA) is perhaps the most widely method for data
dimensionality reduction. A key question in PCA decomposition of data is
deciding how many factors to retain. This manuscript describes a new approach
to automatically selecting the number of principal components based on the
Bayesian minimum message length method of inductive inference. We also derive a
new estimate of the isotropic residual variance and demonstrate, via numerical
experiments, that it improves on the usual maximum likelihood approach.
