Thursday 25 May 2017: Interpolating sea mammal tracks: fusing statistical and nonstatistical models
Jim Zidek - University of British Columbia
Many biologging studies deploy biologgers equipped with magnetometers and accelerometers to record animal movements at infra-second frequencies, thus allowing their tracks to be to be reconstructed at ?high-resolution by dead reckoning (DR). But stochastic factors limit the accuracy of the DR paths. So a conventional (but ad hoc) method was developed, which uses irregularly observed GPS points and simply shifts the DR paths to pass through them. While appealing simple, the conventional method lacks the stochastic foundation that enables quantitative uncertainty statements about the true path to be made. The Bayesian melding (BM) approach provides such a foundation for melding model (the DR path) with data (the GPS measurements). However that approach is computational intensive at the best of times and here the challenges are daunting, due the high dimensional data records. Our implementation of the BM uses a Brownian Bridge process to combine the fine-resolution (but seriously biased) DR path and the sparse (but precise) GPS measurements. But several key approximations and a conditional independence property of the Brownian Bridge process were needed to make it work. A cross-validatory assessment of the method will be described and show that the BM works pretty well, when applied to data obtained from northern fur seals (Callorhinus ursinus) foraging in the Bering Sea. The GPS corrected high-resolution path also revealed that the total distance traveled by the fur seals was much greater than that calculated by simply joining the dots (linear interpolation of the GPS observations)! Use of an integrated Ornstein-Ohlenbeck process was explored and found unsatisfactory leading to our generalized Ornstein-Uhlenbeck process that seems promising and these results will also be described.