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On modeling animal movements using Brownian motion with measurement error
Author(s) -
Pozdnyakov Vladimir,
Meyer Thomas,
Wang Yu-Bo,
Yan Jun
Publication year - 2014
Publication title -
ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.144
H-Index - 294
eISSN - 1939-9170
pISSN - 0012-9658
DOI - 10.1890/13-0532.1
Subject(s) - brownian bridge , statistical physics , brownian motion , fractional brownian motion , mathematics , likelihood function , diffusion process , noise (video) , markov chain , computer science , algorithm , estimation theory , statistics , physics , artificial intelligence , knowledge management , innovation diffusion , image (mathematics)
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.