标题： 一个马尔可夫切换离散时间霍克斯过程：应用于蝙蝠行为的监测 显示英文标题

标题： A Markov switching discrete-time Hawkes process: application to the monitoring of bats behavior

摘要： 在过去几十年中，由于能够捕捉不同的依赖结构，Hawkes过程已成为建模时间事件的流行框架。 本工作的目标是建模蝙蝠用于回声定位发出的通话序列，其模式已知会根据动物的活动而变化。 该模型的新颖性在于结合了来自过去事件的Hawkes类型依赖关系，以及一个编码蝙蝠行为变化的潜在变量。 更准确地说，我们考虑了一个离散时间版本的Hawkes过程，具有指数核，其中移民项根据一个潜在的马尔可夫链变化。 我们证明了该模型是可识别的，并且可以重新表述为具有泊松发射的隐马尔可夫模型。 基于这些特性，我们展示了可以使用EM算法进行模型参数的最大似然推断，该算法涉及递归的M步。 模拟研究展示了我们方法在估计参数、恢复隐藏状态数量和对轨迹的每个区间进行分类方面的性能。 最后，我们说明了所提出的建模方法在区分蝙蝠不同行为中的应用，这是基于它们叫声的记录。 显示英文摘要

摘要： Over the past few decades, the Hawkes process has become a popular framework for modeling temporal events thanks to its flexibility to capture different dependency structures. The objective of this work is to model call sequences emitted by bats for echolocation, whose patterns are known to change depending on the animal's activity. The novelty of the model lies in the combination of a Hawkes-type dependency from past events, as well as a latent variable that encodes changes in bat behavior. More precisely, we consider a discrete-time version of the Hawkes process, with an exponential kernel, where the immigration term varies according to a latent Markov chain. We prove that this model is identifiable and can be reformulated in terms of a Hidden Markov Model, with Poisson emissions. Based on these properties, we show that maximum likelihood inference of the model parameters can be performed using an EM algorithm, which involves a recursive M-step. A simulation study demonstrates the performance of our approach method for estimating the parameters, recovering the number of hidden states and classifying each bin of the trajectory. Finally, we illustrate the use of the proposed modeling to distinguish different behaviors of bats, based on the recording of their cries.