Bayesian statisical estimation for nonlinear dynamic systems in the marine environmental sciences

海洋环境科学的数学模型体现了这些系统如何运作的理论概念。洋流的模型已经建立得很好了，海洋生物学的模型也正在出现。这些数学模型通常又大又复杂，通常在计算机上进行数值求解。技术进步带来了海洋系统的测量革命，出现了物理、生物和化学变量的新传感器，以及卫星、自动海洋观测站和水下自动潜航器等新的观测平台。来自这些仪器的环境数据很复杂。一个主要的挑战是如何有效地利用来自模式预测和观测的信息来最佳地确定海洋的状态(这个问题被称为数据同化)。这项研究计划关注于将先进的统计方法应用于数据同化问题。数学建模和测量技术已经远远超过了将模型和数据结合在一起的统计方法的发展。这项拟议的研究方案旨在通过开发和应用融合这些不同信息来源的先进统计方法来解决这一知识差距。这些方法依赖于计算蒙特卡罗方法和贝叶斯推理。它们为解决海洋环境系统的数据同化问题提供了一类新的一般统计方法，并最终有助于改进海洋环境预测。

Mathematical models for the marine environmental sciences embody theoretical notions of how these systems operate. Models are well established for ocean currents, and are emerging for ocean biology. These mathematical models are typically large and complex, and generally solved numerically on a computer. Technological advances have led to a measurement revolution for marine systems in the form of new sensors for physical, biological and chemical variables, as well as new observing platforms such as satellites, automated ocean observatories, and underwater autonomous vehicles. The environmental data coming from these instruments is complex. A major challenge is how to effectively use the information coming from both model predictions and observations to optimally determine the state of the ocean (a problem that has come to be known as data assimilation).This research program is concerned with applying advanced statistical methods to the data assimilation problem. Mathematical modeling and measurement technology have far outstripped the development of statistical methods for combining models and data. This proposed research program intends to address this knowledge gap through the development and application of advanced statistical methods that fuse these different sources of information. These approaches rely on computational Monte Carlo methods and Bayesian reasoning. They provide a new class of general statistical methods for addressing the data assimilation problem for marine environmental systems, and ultimately contribute towards improved marine environmental prediction.