10.6084/M9.FIGSHARE.C.3306450.V1
Vladimir Pozdnyakov
Vladimir
Pozdnyakov
Thomas Meyer
Thomas
Meyer
Yu-Bo Wang
Yu-Bo
Wang
Jun Yan
Jun
Yan
On modeling animal movements using Brownian motion with measurement error
<p>Modeling animal movements with Brownian motion (or more generally by a Gaussian process) has a long tradition in ecological studies. The recent Brownian bridge movement model (BBMM), which incorporates measurement errors, has been quickly adopted by ecologists because of its simplicity and tractability. We discuss some nontrivial properties of the discrete-time stochastic process that results from observing a Brownian motion with added normal noise at discrete times. In particular, we demonstrate that the observed sequence of random variables is not Markov. Consequently the expected occupation time between two successively observed locations does not depend on just those two observations; the whole path must be taken into account. Nonetheless, the exact likelihood function of the observed time series remains tractable; it requires only sparse matrix computations. The likelihood-based estimation procedure is described in detail and compared to the BBMM estimation.</p>
Other environmental sciences not elsewhere classified
Ecology not elsewhere classified
Wiley
2016
2016-08-10
2019-08-20
Collection
10.6084/m9.figshare.c.3306450
CC BY 4.0