David Brillinger, University of California, Berkeley
A Unified Approach to Modelling Trajectories
The talk will concern the employment of stochastic gradient systems in the modeling and statistical analysis of biological and ecological processes of moving particles. The work is stimulated by scientific questions and data sets of the movements of elk and deer (at the Starkey Experimental Reserve in Oregon), of elephant seals (off the California coast), of Hawaiian monk seals, and of the soccer ball in a game. Stochastic models and data analyses will be presented. The models are motivated by setting down a potential function leading to a stochastic differential equation. The estimated potential function may be used for: simple description, summary, comparison, simulation, prediction, model appraisal, bootstrapping, and employed for estimating quantities of interest. Explanatories, attractors and repellors, may be included in the potential function directly.
Louis-Paul Rivest, UniversitÃ© Laval
A Directional Model for the Determination of the Anatomical Axes of the Ankle Joint
The human ankle connects the foot and the shank. This joint is a complex kinematics system that supports two types of motion. Two rotation axes are needed to describe the motion of the ankle joint. Estimating the directions of these two axes is of interest in clinical biomechanics since they carry diagnostics information for abnormal locomotion. This estimation can be done by recording the 3D positions of markers attached to the foot and the lower leg of a subject moving his foot around his ankle. The markersâ€™ coordinates are transformed into sequences of 3x1 translation vector and of 3x3 rotation matrices giving the relative positions of the foot with respect to the shank. The rotation axes are then estimated by fitting a directional model to the sequence of 3x3 rotation matrices. After reviewing this experimental protocol, the presentation focuses on statistical issues surrounding the estimation of the two axes. Data analyses will illustrate the main findings. This is joint work with Michael Pierrynowski, McMaster University and Sophie Baillargeon, UniversitÃ© Laval.
Jerry Lawless, University of Waterloo
Some Challenges in Assessing Goodness of Fit
As models or data collection become more complex, we tend to rely mainly on model expansion in order to assess a model's "fit." That is, a model of interest is embedded in a larger family, within which it may be tested. However, it is desirable also to have model checks that are more transparent, along the lines of plotting techniques and classical goodness of fit tests. In this talk we consider some problems involving complex processes, missing data, response-selective sampling, and unobservable random effects. The objective is to describe interesting areas where research on goodness of fit methodology is warranted.
Richard Lockhart, Simon Fraser University