Sequential Monte Carlo methods for applications in high dimensions.

时至今日，序贯蒙特卡罗(SMC)方法被广泛地应用于各个学科，以利用来自输入数据的信息来校准数学模型并对复杂的非线性随机系统进行预测。SMC方法已经成功地应用于计量经济学、通信、目标跟踪、计算机视觉、机器人和生物学等多个领域。他们将推断随机系统的未知参数和给定数据流的系统(信号)的未观察状态。然而，众所周知，标准的SMC方法不能处理大气科学、海洋学、水文学和信号处理等领域中出现的重要的高维问题，因为它们的计算成本随着系统状态空间的维度呈指数级快速增长。这一点非常重要，因为目前在高维中使用的替代方法不能完全捕获应用中出现的非线性模型动态，并且可能对此类非线性场景中的不确定性或预测给出不准确的估计。

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.