Reduced rank regression in Bayesian FDA

In functional data analysis (FDA) it is of interest to generalize techniques 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 interpolation splines to represent functions parsimoniously and ‡exibly; (ii) latent variable models for probabilistic principal components analysis or canonical correlation analysis of the corresponding coe¢ cients. 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 explorative data analysis. The performance of the approach is illustrated with synthetic and real data sets. As detailed in the table of contents the paper has a “vertical” structure corresponding to topics in data analysis and de…ning the sequence of chapters and a “horizontal” structure referring to the most important special cases of the proposed model: FCCA, functional regression, scalar prediction, classi…cation. Within chapters the special cases are addressed in turn such that a reader interested only in a special application of the model may skip the other sections.