Statistical models for dependent trajectories with application to animal movement
Date
2017
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Abstract
In this dissertation, I present novel methodology to study the way animals interact with each other and the landscape they inhabit. I propose two statistical models for dependent trajectories in which depedencies among paths arise from pairwise relationships defined using latent dynamic networks. The first model for dependent trajectories is formulated in a discrete-time framework. The model allows researchers to make inference on a latent social network that describes pairwise connections among actors in the population, as well as parameters that govern the type of behavior induced by the social network. The second model for dependent trajectories is formulated in a continuous-time framework and is motivated primarily by reducing uncertainty in interpolations of the continuous trajectories by leveraging positive dependence among individuals. Both models are used in applications to killer whales. In addition to the two models for multiple trajectories, I introduce a new model for the movement of an individual showing a preference for areas in a landscape near a complex-shaped, dynamic feature. To facilitate estimation, I propose an approximation technique that exploits of locally linear structure in the feature of interest. I demonstrate the model for the movement of an individual responding to a dynamic feature, as well as the approximation technique, in an application to polar bears for which the changing boundary of Arctic sea ice represents the relevant dynamic feature.