Stochastic modelling and inference for some ecological systems

一些生态系统的随机建模和推理

• 批准号: 327006-2006
• 负责人: Nkurunziza, Severien
• 金额: $ 0.58万
• 依托单位: University of Windsor
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2006
• 资助国家: 加拿大
• 起止时间: 2006-01-01 至 2007-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=334375
• 关键词: Stochastic; modelling; inference; some; ecological

We consider inference problems concerning the parameters of a deterministic Lotka-Volterra system of differential equations, which describes the ecological interaction between prey and predator. So far, we generalized the Froda and Colavita (2005) method where the evolution of predator-prey interactions is modeled as the trajectory of a Lotka-Volterra system plus a random error, which is an independent and identically distributed process. In Froda and Nkurunziza (2005), as well as in my thesis, we assume that the components error follow Ornstein-Uhlenbeck processes with special dependence structure. We present mathematical properties, used in inference, which are deduced from this dependence structure. Moreover, we show that these more general and flexible assumptions allow us to improve the prediction of the population sizes (prey and predators). In the thesis and the related papers, we propose an estimator of the parameters of the deterministic system of differential equations, as well as the most powerful tests concerning these parameters. Furthermore, we study the asymptotic properties of the proposed estimator and tests. So far, we have used only frequentist inference. Thus, in the short and medium term, I consider improving the estimation method as well as the prediction of the population sizes by using Bayes methods. Namely, I will use a noninformative prior distributions for the parameters. As in our previous work, I will establish the asymptotic properties of the new estimators and tests by using ergodic theory. A long-term objective is to develop new statistical methods based only on diffusion processes. In the diffusion processes approach, I will consider differential stochastic equations corresponding to deterministic equations. This approach should allow us to drive maximum likelihood estimators that are, under some conditions, consistent, unbiased, with uniformly minimum variance. Moreover, this approach could be the most appropriate one for other ecological models which are more general than the two-species predator-prey system. In fact, I plan to deal with other ecological models such as two- or three-species in the presence of social phenomena.

我们考虑有关确定性 Lotka-Volterra 微分方程组参数的推理问题，该微分方程组描述了猎物和捕食者之间的生态相互作用。到目前为止，我们概括了Froda和Colavita（2005）的方法，其中捕食者-猎物相互作用的演化被建模为Lotka-Volterra系统的轨迹加上随机误差，这是一个独立且同分布的过程。在 Froda 和 Nkurunziza (2005) 以及我的论文中，我们假设分量误差遵循具有特殊依赖结构的 Ornstein-Uhlenbeck 过程。我们提出了用于推理的数学属性，这些属性是从这种依赖结构中推导出来的。此外，我们表明，这些更普遍和灵活的假设使我们能够改进对种群规模（猎物和捕食者）的预测。在论文和相关论文中，我们提出了微分方程确定性系统参数的估计，以及关于这些参数的最强大的检验。此外，我们研究了所提出的估计量和测试的渐近特性。到目前为止，我们只使用了频率论推理。因此，在中短期内，我考虑改进估计方法以及使用贝叶斯方法对人口规模的预测。也就是说，我将使用参数的非信息先验分布。与我们之前的工作一样，我将使用遍历理论建立新估计量和检验的渐近性质。长期目标是开发仅基于扩散过程的新统计方法。在扩散过程方法中，我将考虑与确定性方程相对应的微分随机方程。这种方法应该允许我们驱动最大似然估计器，这些估计器在某些条件下是一致的、无偏的、具有一致的最小方差。此外，这种方法可能是最适合其他生态模型的方法，这些模型比两种捕食者-被捕食者系统更通用。事实上，我计划处理其他生态模型，例如存在社会现象的两个或三个物种。