Inference on the state process of periodically inhomogeneous hidden Markov models for animal behavior
Jan-Ole Koslik, Carlina C. Feldmann, Sina Mews, Rouven Michels, Roland Langrock
The Annals of Applied Statistics · 2025 · Volume 19 · Issue 4
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. Crucially, we demonstrate that the dwell-time distributions of periodically inhomogeneous HMMs can deviate substantially from a geometric distribution, thus compensating biologically unrealistic consequences of the Markov property. We use the novel inference and model-checking tools to investigate changes in the diel activity patterns of fruit flies in response to changing light conditions.
Keywords
Markov chain; seasonality; sojourn time; stationary distribution; statistical ecology; time series;
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