Open Access
December 2019 New formulation of the logistic-Gaussian process to analyze trajectory tracking data
Gianluca Mastrantonio, Clara Grazian, Sara Mancinelli, Enrico Bibbona
Ann. Appl. Stat. 13(4): 2483-2508 (December 2019). DOI: 10.1214/19-AOAS1289


Improved communication systems, shrinking battery sizes and the price drop of tracking devices have led to an increasing availability of trajectory tracking data. These data are often analyzed to understand animal behavior.

In this work, we propose a new model for interpreting the animal movent as a mixture of characteristic patterns, that we interpret as different behaviors. The probability that the animal is behaving according to a specific pattern, at each time instant, is nonparametrically estimated using the Logistic-Gaussian process. Owing to a new formalization and the way we specify the coregionalization matrix of the associated multivariate Gaussian process, our model is invariant with respect to the choice of the reference element and of the ordering of the probability vector components. We fit the model under a Bayesian framework, and show that the Markov chain Monte Carlo algorithm we propose is straightforward to implement.

We perform a simulation study with the aim of showing the ability of the estimation procedure to retrieve the model parameters. We also test the performance of the information criterion we used to select the number of behaviors. The model is then applied to a real dataset where a wolf has been observed before and after procreation. The results are easy to interpret, and clear differences emerge in the two phases.


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Gianluca Mastrantonio. Clara Grazian. Sara Mancinelli. Enrico Bibbona. "New formulation of the logistic-Gaussian process to analyze trajectory tracking data." Ann. Appl. Stat. 13 (4) 2483 - 2508, December 2019.


Received: 1 April 2019; Revised: 1 July 2019; Published: December 2019
First available in Project Euclid: 28 November 2019

zbMATH: 07160947
MathSciNet: MR4037438
Digital Object Identifier: 10.1214/19-AOAS1289

Keywords: continuous-time hidden Markov model , coregionalization , Invariance , Wolf data

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.13 • No. 4 • December 2019
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