The study of the interaction among species is an active area of research in Ecology. In particular, it is of interest to evaluate the overlap of their ecological niches. Temporal activity is one of the niche’s axes most commonly used to explore ecological segregation among animal species, and many contributions focus on the overlap of this variable. Once the information of the temporal activity is obtained in the wild, the data is treated as a random sample. There exist different methods to estimate the overlap. Specifically, in the case of two species, one possibility is to estimate the density of the temporal activity of each species and then evaluate the overlap between these density functions. This leads naturally to the analysis of circular data. Most of the procedures currently in use impose some rather restrictive assumptions on the probabilistic models used to describe the phenomena, and only provide approximate measures of the uncertainty involved in the process. In this article, we propose a Bayesian nonparametric approach which incorporates a well-defined noninformative prior. We take advantage of the data structure to define such a prior in terms of the predictive distribution. To the best of our knowledge, this is a novel approach. Our procedure is compared with a well-known method using simulated data, and applied to the analysis of real camera-trap data concerning two mammalian species from the El Triunfo biosphere reserve (Chiapas, Mexico).

中文翻译：

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日常动物活动模式重叠的贝叶斯非参数推断

物种间相互作用的研究是生态学研究的活跃领域。尤其值得关注的是评估其生态位的重叠。时间活动是最常用于探索动物物种之间生态隔离的利基坐标轴之一，许多贡献集中于该变量的重叠。一旦在野外获得了时间活动的信息，就将数据视为随机样本。存在估计重叠的不同方法。具体来说，在两个物种的情况下，一种可能性是估计每个物种的时间活动的密度，然后评估这些密度函数之间的重叠。这自然导致对循环数据的分析。当前使用的大多数程序对用于描述现象的概率模型强加了一些相当限制性的假设，并且仅提供了过程中涉及的不确定性的近似度量。在本文中，我们提出了一种贝叶斯非参数方法，该方法结合了定义明确的非信息先验。我们利用数据结构来根据预测分布定义这种先验。就我们所知，这是一种新颖的方法。我们的程序与使用模拟数据的众所周知的方法进行了比较，并被用于分析涉及两个哺乳动物物种的真实相机捕获数据。我们提出了一种贝叶斯非参数方法，该方法结合了定义明确的非信息先验。我们利用数据结构来根据预测分布定义这种先验。就我们所知，这是一种新颖的方法。我们的程序与使用模拟数据的众所周知的方法进行了比较，并被用于分析涉及两个哺乳动物物种的真实相机捕获数据。我们提出了一种贝叶斯非参数方法，该方法结合了定义明确的非信息先验。我们利用数据结构来根据预测分布定义这种先验。就我们所知，这是一种新颖的方法。我们的程序与使用模拟数据的众所周知的方法进行了比较，并被用于分析涉及两个哺乳动物物种的真实相机捕获数据。El Triunfo生物圈保护区（墨西哥恰帕斯）。