🤖 AI Summary
Modeling periodic dynamics—such as circadian and seasonal rhythms—in animal behavior studies poses challenges for conventional homogeneous hidden Markov models (HMMs), which assume stationarity and fail to capture time-varying latent state distributions.
Method: We propose a novel statistical inference framework for periodic non-homogeneous HMMs, analytically deriving the periodic unconditional state distribution and time-varying sojourn-time distribution for the latent state process. Integrating probability theory and stochastic processes, our approach unifies interpretable modeling, rigorous parameter inference, and model diagnostics within a single coherent framework.
Contribution/Results: Applied to Drosophila photobehavioral sensor data, the method successfully identifies dynamic reconfiguration of circadian activity patterns under light-environment perturbations. It demonstrates strong validity, robustness to ecological noise, and biological interpretability in real-world sensor-based behavioral analysis—overcoming key limitations of standard HMMs in non-stationary biological time series.
📝 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.
