Mathematical Sciences: Statistical Inference for Some Dynamic Phenomena

首席调查员将开发随机模型和统计方法，以处理记录的关于在时间和/或空间上演变的现象的数据。由于数据的复杂性，实质性领域的专题将在建模和分析中发挥关键作用；然而，预计所开发的技术将广泛适用。对于复杂的随机函数，将开发普通随机变量的各种技术。要研究的一些特殊问题是：1)核磁共振波谱基本的双线性系统的参数估计和输入信号设计，2)用于模拟和识别适用于放电神经细胞网络的相互作用点过程集合的结构的技术发展。对于所研究的问题，研究者将获得理论和应用两方面的结果。首席研究人员将开发随机模型和统计方法，以处理记录的关于在时间和/或空间上演变的现象的数据。由于数据的复杂性，实质性领域的专题将在建模和分析中发挥关键作用；然而，预计所开发的技术将广泛适用。对于复杂的随机函数，将开发普通随机变量的各种技术。要研究的一些特殊问题是：1)核磁共振波谱基本的双线性系统的参数估计和输入信号设计，2)用于模拟和识别适用于放电神经细胞网络的相互作用点过程集合的结构的技术发展。对于所研究的问题，研究者将获得理论和应用两方面的结果。

The principal investigator will develop stochastic models and statistical methods for handling data recorded on phenomena evolving in time and/or distributed in space. Because of the complexity of the data, the subject matter of the substantive field will play a crucial role in modelling and analysis; however it is anticipated that the techniques developed will be broadly applicable. Variants of techniques for ordinary random variables will be developed for complex random functions. Some of the particular problems to be studied are: 1) parameter estimation and input signal design for the bilinear system basic to nuclear magnetic resonance spectroscopy, 2) technique development for modelling and discerning the structure of collections of interacting point processes as applicable to networks of firing nerve cells. The investigator will obtain both theoretical and applied results for the problems studied. The principal investigator will develop stochastic model and statistical methods for handling data recorded on phenomena evolving in time and/or distributed in space. Because of the complexity of the data, the subject matter of the substantive field will play a crucial role in modelling and analysis; however it is anticipated that the techniques developed will be broadly applicable. Variants of techniques for ordinary random variables will be developed for complex random functions. Some of the particular problems to be studied are: 1) parameter estimation and input signal design for the bilinear system basic to nuclear magnetic resonance spectroscopy, 2) technique development for modelling and discerning the structure of collections of interacting point processes as applicable to networks of firing nerve cells. The investigator will obtain both theoretical and applied results for the problems studied.