In functional data analysis (FDA) it is of interest to generalize tech-
niques of multivariate analysis like canonical correlation analysis or regression to
functions which are often observed with noise. In the proposed Bayesian approach
to FDA two tools are combined: (i) a special Demmler-Reinsch like basis of in-
terpolation splines to represent functions parsimoniously and
exibly; (ii) latent
variable models initially introduced for probabilistic principal components anal-
ysis or canonical correlation analysis of the corresponding coecients. In this
way partial curves and non-Gaussian measurement error schemes can be handled.
Bayesian inference is based on a variational algorithm such that computations are
straight forward and fast corresponding to an idea of FDA as a toolbox for explo-
rative data analysis. The performance of the approach is illustrated with synthetic
and real data sets.