Motivated by the dynamic modeling of relative abundance data in ecology, we introduce a general approach to model time series on the simplex. Our approach is based on a general construction of infinite memory models, called chains with complete connections. Simple conditions ensuring the existence of stationary paths are given for the transition kernel that defines the dynamic. We then study in details two specific examples with a Dirichlet and a multivariate logistic-normal conditional distribution. Inference methods can be based on either likelihood maximization or on some convex criteria that can be used to initialize likelihood optimization. We also give an interpretation of our models in term of additive perturbations on the simplex and relative risk ratios which are useful to analyze abundance data in ecosystems. An illustration concerning the evolution of the distribution of three species of Scandinavian birds is provided.
翻译:在生态相对丰度数据动态模型的推动下,我们引入了一种通用方法,在简单x上模拟时间序列。我们的方法基于无限内存模型的一般构建,称为全连链。为定义动态的过渡内核提供了确保固定路径存在的简单条件。然后我们详细研究两个具体例子,用分流和多变后勤-正常的有条件分布。推论方法可以基于可能性最大化或一些可用于初始化可能性优化的同流标准。我们还用简单x和相对风险比率的添加干扰来解释我们的模型,这些模型有助于分析生态系统中的丰度数据。提供了斯堪的纳维亚鸟类三种物种分布的演变图解。