Modelling functional data with hierarchical hidden Markov models: Applications to animal movement
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Modern biologging sensors can record sequences of curves at very high frequencies, allowing researchers to observe biological processes such as animal movement at extremely fine scales. High-frequency data sets can exhibit state-switching, multi-scale dependence structures that are difficult to model with standard methods in functional data analysis. Inspired by data collected from a northern resident killer whale (Orcinus orca), we describe a hierarchical framework that treats curves as observations from a hidden Markov model. Each curve’s distribution is defined by a fine-scale model whose parameters depend upon a coarse-scale latent process. Through simulations, we show that our model produces more interpretable state estimates and more accurate parameter estimates compared to existing methods. We also consider several computational challenges when modelling state-switching functional data with hidden Markov models.