Principle Component Analysis is a simple tool to obtain linear models for

stochastic data and is used both for a data reduction or equivalently noise elim-

ination and for data analysis. Principle Component Analysis ts a multivariate

Gaussian distribution to the data, and the typical method is by using the log-

likelihood estimator. However for small sets of high dimensional data, the log-

likelihood estimator is often far from convergence, and therefore reliable models

must be obtained by use of prior information. In this paper, we will examine

an earlier work on reconstructing missing data using statistical knowledge and

regularization, we will show the circumstances for which this is equivalent to

a Bayes estimation, we will give an expository presentation of Bayes Principle

Component Analysis for a range of exponential type priors, and we will develop

algorithms for their estimate.