Scaled von Mises-Fisher distributions and regression models for palaeomagnetic directional data

Friday June 8, 2pm, Carslaw 173

Janice Scealy
Australian National University, Research School of Finance, Actuarial Studies & Statistics

Scaled von Mises-Fisher distributions and regression models for palaeomagnetic directional data

We propose a new distribution for analysing palaeomagnetic directional data that is a novel transformation of the von Mises-Fisher distribution. The new distribution has ellipse-like symmetry, as does the Kent distribution; however, unlike the Kent distribution the normalising constant in the new density is easy to compute and estimation of the shape parameters is straightforward. To accommodate outliers, the model also incorporates an additional shape parameter which controls the tail-weight of the distribution. We also develop a general regression model framework that allows both the mean direction and the shape parameters of the error distribution to depend on covariates. To illustrate, we analyse palaeomagnetic directional data from the GEOMAGIA50.v3 database. We predict the mean direction at various geological time points and show that there is significant heteroscedasticity present. It is envisaged that the regression structures and error distribution proposed here will also prove useful when covariate information is available with (i) other types of directional response data; and (ii) square-root transformed compositional data of general dimension. This is joint work with Andrew T. A. Wood.

Dr Janice Scealy is a senior lecturer in statistics in the Research School of Finance, Actuarial Studies and Statistics, ANU and she is currently an ARC DECRA fellow. Her research interests include developing new statistical analysis methods for data with complicated constraints, including compositional data defined on the simplex, spherical data, directional data and manifold-valued data defined on more general curved surfaces.