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（HMMs）在统计生态学领域日益普及，成为基于复杂传感器数据研究动物行为的天然工具。相关分析有时会明确关注周期性变化（例如通过量化日周期内的活动分布或迁徙行为等季节性变化），且在建模时均需考虑此类周期性因素。针对包含周期性分量的HMMs，我们建立了重要的数学性质，使得对周期性变化进行全面统计推断成为可能，同时为模型构建与检验提供了理论指导。具体而言，我们推导了周期性变化的无条件状态分布、时变状态驻留时间分布及整体状态驻留时间分布——当推断重点聚焦于状态过程的动态特性时，这些分布均具有关键意义。我们运用相关的新型推断与模型检验工具，研究了果蝇在光照条件变化下昼夜活动模式的改变。