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National Institute for Applied Statistics Research Australia Seminar Series
February 11, 2019 @ 2:30 pm - 3:30 pm
Professor Andrew Wood (University of Nottingham)
Regression modelling using the scaled von Mises-Fisher distribution: an example of manifold-valued response data
The talk will begin with a brief review of manifold-valued response data, key examples of which include compositional data, directional data, shape data, size-and-shape data, rotations and positive definite matrices. These various types of data, all of which have non-Euclidean structure, arise naturally in many areas of science and technology, and developing effective methods for analysing such data, e.g. through the construction of suitable regression models, is of major practical importance. The talk will then focus on a particular approach to regression modelling of directional data. The best-known distribution on the sphere for statistical purposes is the Fisher, or von Mises-Fisher, distribution. However, this distribution possesses rotational symmetry, which is too strong an assumption for many applications. Here we present a new distribution, called the scaled von Mises-Fisher (SvMF) distribution, which has ellipse-like contours yet has a simple normalising constant. A main goal for developing this distribution is to use it for regression modelling of paleomagnetic data with a directional response. The analysis of such data using a SvMF-based regression model will be described.
Most of the talk is based on joint work with Dr Janice Scealy (ANU).