Sequential Monte Carlo methods for applications in high dimensions.

顺序蒙特卡罗（SMC）方法现在被广泛应用于校准数学模型和对复杂非线性随机系统进行预测，使用来自输入数据的信息。SMC方法已成功应用于计量经济学、通信、目标跟踪、计算机视觉、机器人和生物学等多个领域。他们将根据给定的数据流推断随机系统的未知参数和系统的未观察状态（“信号”）。然而，众所周知，标准SMC方法无法解决大气科学、海洋学、水文学和信号处理等领域出现的重要高维问题，因为它们的计算成本随着系统状态空间的维数呈指数级增长。所提出的研究将调查和开发先进的SMC方法，提高高维算法效率，使SMC方法在这种情况下具有实际意义。这是非常重要的，因为目前在高维中使用的替代方法不能完全捕获应用中产生的非线性模型动力学，并且可以在这种非线性场景中给出不确定性的不准确估计或预测。

Sequential Monte Carlo (SMC) methods are nowadays routinely employed across a wide range of disciplines to calibrate mathematical models and carry out forecasting about complex non-linear stochastic systems, using information from incoming data. SMC methods have been successfully applied in such diverse areas as econometrics, communications, target tracking, computer vision, roboting and biology. They will infer about unknown parameters of stochastic systems and unobserved states of the systems (the "signal") given streams of data. However, it is a common knowledge that standard SMC methods cannot tackle important high-dimensional problems, arising in fields such as atmospheric sciences, oceanography, hydrology and signal processing, as their computational cost has been found to increase exponentially fast with the dimension of the state space of the system.The proposed research will investigate and develop advanced SMC methods of improved algorithmic efficiency in high dimensions, rendering SMC methodology practically relevant in such contexts. This is of high importance as alternative methods currently used in high dimensions cannot fully capture non-linear model dynamics arising in applications, and can give inaccurate estimates of uncertainty or forecasts in such non-linear scenarios.