John ASTON, University of Cambridge

Functional Data Analysis concerns the statistical study of curves and surfaces. An extension, Functional Object Data Analysis, looks at the statistical analysis of curves and surfaces which live in restricted spaces, such as on manifolds. One particular example of these are the covariance functions associated with the underlying curves. These positive definite operators can often be of interest in their own right, yet standard functional data models are not appropriate due to the positive definite space they are constrained to lie in.

Statistical models for both traditional functional data and separable positive definite models will be discussed, particularly in regards to the modelling of phonetic data. Acoustic phonetic data from different dialects or languages can be associated with both mean and covariance functions, and models used to try to interpolate and extrapolate sounds from one language to another. We will demonstrate that by considering the spaces where these sounds lie, it is possible to turn a speaker from one language to another, and literally listen to our statistical analysis. We will also show that we can use these ideas to determine whether trees are good representations of historical transmission of spoken language.

[Main Co-authors: John Coleman (Oxford), Davide Pigoli (Cambridge), Nathaniel Shiers (Warwick) and Shahin Tavakoli (Cambridge)]