Inference on the state process of periodically inhomogeneous hidden Markov models for animal behavior

TL;DR

This paper develops mathematical tools for inference on periodically inhomogeneous hidden Markov models, enabling detailed analysis of animal behavior patterns over daily or seasonal cycles, with applications to fruit fly activity.

Contribution

It introduces new theoretical results for HMMs with periodic components, including state and dwell-time distributions, aiding model building and checking.

Findings

Derived the periodic state distribution and dwell-time distributions.

Applied methods to analyze diel activity changes in fruit flies.

Provided inference tools for models with periodic variation.

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.