Modeling the effects of high-dimensional covariates on 3D kinematics
Julia Wrobel (joint work with Jeff Goldsmith)

We assess methods for modeling 3D kinematics of objects, with the goal of relating trajectories to potentially high-dimensional covariates. Our work is motivated by novel data from an experiment exploring the relationship between neural firing rates and hand trajectories of mice performing a reaching task while under neurological assessment. We present results from functional linear concurrent, function-on-function regression models, and a Kalman filter. The functional models allow for different time-lag relationships between hand position and neural activity, and the Kalman filter is a flexible Bayesian probabilistic framework treating hand position and velocity as a Markov process influenced by perturbations in neural activity. The input variables are firing rates of 25 neurons measured concurrent with the hand reaching activity. This sparse and complex input requires careful attention to signal extraction; we employ dimension reduction and variable selection techniques to optimize understanding of the relationship between hand position and neural activity.
Key Words: trivariate functional data, functional regression, Kalman filter