Inference on the state process of periodically inhomogeneous hidden Markov models for animal behavior
arxiv(2023)
Abstract
Over the last decade, hidden Markov models (HMMs) have become increasingly
popular in statistical ecology, where they constitute natural tools for
studying animal behavior based on complex sensor data. Corresponding analyses
sometimes explicitly focus on - and in any case need to take into account -
periodic variation, for example by quantifying the activity distribution over
the daily cycle or seasonal variation such as migratory behavior. For HMMs
including periodic components, we establish important mathematical properties
that allow for comprehensive statistical inference related to periodic
variation, thereby also providing guidance for model building and model
checking. Specifically, we derive the periodically varying unconditional state
distribution as well as the time-varying and overall state dwell-time
distributions - all of which are of key interest when the inferential focus
lies on the dynamics of the state process. We use the associated novel
inference and model-checking tools to investigate changes in the diel activity
patterns of fruit flies in response to changing light conditions.
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