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M. Templ:
"Compositional data analysis, probability density functions and functional data analysis. With an application to spatio-temporal population pyramids";
Talk: IDP Kolloquium, Winterthur; 2017-03-01.

The presentation consists of two (almost) separate parts.
In the first part of the presentation, compositional data and compositional data analysis are introduced with catchy examples and data sets. For this purpose resources of the Springer-book "Applied Compositional Data Analysis" (Filzmoser, Hron, Templ, 2018, DOI: 10.1007/978-3-319-96422-5) are used.
In the second part we want to deal with a new topic, which is not yet noticed and has never been dealt with in any textbook or monograph.
As compositional data, functional data occurs frequently in practice. For example, a child is often measured for weight and height, and these measurements are compared over time with the weight and height time-depended curves of other children. Even the Covid-19 infection data measured over time are functional data, even if the numbers are periodically reported only once a day.
We want to take a closer look at functional data analysis, which is essentially based on probability density functions. Probability density functions are frequently used in practice in many areas of research, and everybody at IDP got in touch with them as well as our students (have to) learn the concept of a density.
As functional compositions, densities carry primarily relative information. As such, standard methods of functional data analysis (FDA) are not appropriate for their statistical processing. The specific features of density functions are accounted for in Bayes spaces, which result from the generalization to the infinite dimensional setting of the Aitchison geometry for compositional data. The aim of the presentation is to provide a brief outline of a concise methodology for functional principal component analysis of densities based on compositional data analysis (details in Hron et al., 2018, DOI: 10.1016/j.csda.2015.07.007). But we do not want to become too theoretical and show the ideas of the new method using a real-world example of population pyramids in Upper Austria.

Compositional Data Analysis, Functional Data Analysis