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.

翻译：过去十年间，隐马尔可夫模型在统计生态学中日益普及，成为基于复杂传感器数据研究动物行为的自然工具。相应的分析有时明确关注——且无论如何都需要考虑——周期性变化，例如通过量化昼夜周期内的活动分布或迁徙行为等季节性变化。针对包含周期性成分的隐马尔可夫模型，我们建立了重要的数学性质，能够对周期性变化进行全面的统计推断，同时为模型构建和模型检验提供指导。具体而言，我们推导了周期性变化的非条件状态分布，以及时变和整体状态驻留时间分布——当推断重点聚焦于状态过程动态时，这些分布均具有关键研究价值。我们利用相关的新型推断与模型检验工具，研究果蝇在光照条件变化下昼夜活动模式的改变。