Supplementary materials for this article are available at 10.1007/s13253-013-0158-6. Modeling the Diving Behavior of Whales: A Latent-Variable Approach with Feedback and Semi-Markovian Components

Recent years have seen a fast-growing body of literature concerned with the sta-tistical modeling of animal movement in the two horizontal dimensions. On the other hand, there is very little statistical work that deals with animal movement in the vertical dimension. We present an approach that provides an important step in analyzing such data. In particular, we introduce a hidden Markov-type modeling approach for time series comprising the depths of a diving marine mammal, thus modeling movement in the water column. We first develop a baseline Markov-switching model, which is then extended to incorporate feedback and semi-Markovian components, motivated by the observations made for a particular species, Blainville’s beaked whale (Mesoplodon densirostris). The application of the proposed model to the beaked whale data reveals both strengths and weaknesses of the suggested modeling framework. The framework is general enough that we anticipate that it can be used for many other species given minor changes in the model structure