Statistical Inference for Complex Dynamical Models

复杂动力学模型的统计推断

• 批准号: 356044-2013
• 负责人: Cao, Jiguo
• 金额: $ 1.38万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635758
• 关键词: Statistical; Inference; Complex; Dynamical; Models

Dynamical models describe the rate of change of a dynamical system. They are widely used to elucidate complex systems in many areas including neuroscience, biology, medicine, genetics, ecology, engineering, physics, and finance. While the parameters in dynamical models usually have scientific interpretations, their values are often unknown and can sometimes be difficult to estimate directly. This makes it hard to verify dynamical models by showing how well their solutions fit real data. My long-term objective of the proposed research program is to develop statistical methodologies for estimating parameters in dynamical models from measurements of the dynamical system in the presence of measurement errors. I will work broadly in parameter estimation for dynamical models. My research proposal highlights some interesting research problems motivated by important applications. For example, when the dynamical system has replicative measurements over multiple subjects, each subject may have different but correlated values of model parameters. Then it is of great interest to allow both population parameters (fixed effects) and individual parameters (random effects) in the dynamical model, which is then called a mixed-effects dynamical model. Subjects may have missing group information, in which case the measurements for the dynamical system can be reasonably assumed to follow a mixture distribution. I propose a semiparametric method to estimate mixed-effects dynamical models from mixture-distributed data. Another research problem arises when parameters in dynamical models depend on some characters (covariates) of subjects while these parameters have unknown values. It may be desirable to estimate model parameters and their relationships to those covariates simultaneously. I propose an analysis of variance (ANOVA) approach to detect treatment effects on dynamical systems. My proposed research can potentially be applied to many scientific areas such as agriculture, biology, and genetics.

动力模型描述动力系统的变化率。它们广泛用于阐明神经科学、生物学、医学、遗传学、生态学、工程、物理学和金融等许多领域的复杂系统。虽然动力学模型中的参数通常有科学的解释，但它们的值通常是未知的，有时很难直接估计。这使得很难通过显示其解决方案与真实数据的拟合程度来验证动态模型。我所提出的研究计划的长期目标是开发统计方法，用于在存在测量误差的情况下根据动力系统的测量来估计动力模型中的参数。我将广泛致力于动态模型的参数估计。我的研究计划强调了一些由重要应用引发的有趣的研究问题。例如，当动力系统对多个受试者进行重复测量时，每个受试者可能具有不同但相关的模型参数值。然后，在动态模型中同时允许总体参数（固定效应）和个体参数（随机效应）是非常有趣的，这被称为混合效应动态模型。受试者可能缺少群体信息，在这种情况下，可以合理地假设动力系统的测量遵循混合分布。我提出了一种半参数方法来估计混合分布数据的混合效应动力学模型。当动力学模型中的参数取决于受试者的某些特征（协变量）而这些参数具有未知值时，就会出现另一个研究问题。可能需要同时估计模型参数及其与这些协变量的关系。我提出了一种方差分析（ANOVA）方法来检测治疗对动力系统的影响。我提出的研究有可能应用于农业、生物学和遗传学等许多科学领域。