紧空间上的时间序列，及其在生态学相对丰度数据动态建模中的应用
Time series on compact spaces, with an application to dynamic modeling of relative abundance data in Ecology
AI总结：
本文提出一种基于完全连接链的通用方法，用于在紧空间上建模平稳时间序列，涵盖马尔可夫与非马尔可夫模型，并应用于生态学相对丰度数据的动态分析。
摘要：
受生态学中相对丰度数据动态建模的启发，我们提出了一种通用方法，用于在（相对）紧空间（如欧几里得空间中的超立方体、单纯形或球面）上建模平稳马尔可夫或非马尔可夫时间序列。我们的方法基于一种称为完全连接链的无限记忆模型的通用构造。该通用构造涉及的两个主要组成部分是状态空间上的参数族概率分布以及从状态空间到参数空间的映射。我们的框架涵盖马尔可夫模型、观测驱动模型以及更一般的无限记忆模型。我们给出了确保平稳遍历路径存在且唯一的简单条件。随后，我们更详细地研究了单纯形上两种时间序列模型的统计推断，这两种模型分别基于狄利克雷或多元逻辑斯蒂正态条件分布。最后，我们还讨论了我们的模型在分析生态系统中丰度数据方面的实用性。
英文摘要：
Motivated by the dynamic modeling of relative abundance data in ecology, we introduce a general approach to model stationary Markovian or non Markovian time series on (relatively) compact spaces such as a hypercube, the simplex or a sphere in the Euclidean space. Our approach is based on a general construction of infinite memory models, called chains with complete connections. The two main ingredients involved in our generic construction are a parametric family of probability distributions on the state space and a map from the state space to the parameter space. Our framework encompasses Markovian models, observation-driven models and more general infinite memory models. Simple conditions ensuring the existence and uniqueness of a stationary and ergodic path are given. We then study in more details statistical inference in two time series models on the simplex, based on either a Dirichlet or a multivariate logistic-normal conditional distribution. Usefulness of our models to analyze abundance data in ecosystems is also discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
