厦门大学在职研究生招生网
David Stoffer 教授在厦门大学统计学进行了一场主题为非线性状态空间模型的讲座，在职研究生讲座的主要内容如下：
有没有想过如何在“火星一号”单程火星之旅将实际获得的行星，那里没有清盘时，说金星?跟踪设备将使用非线性状态空间模型。虽然推断线性高斯模型是相当简单的，推理的非线性模型是很困难的，往往依赖于衍生自由数值优化方法。一个有前途的方法，我将讨论的基础上给出的数据隐藏进程的条件分布的颗粒近似。因为两者需要的古典推理这种分配(例如，蒙特卡洛EM型算法)和贝叶斯推理(例如，吉布斯采样)。
粒子的方法是连续重要性采样(SIS)的延伸。虽然SIS算法已自20世纪70年代初称，其在非线性问题的使用仍然在很大程度上被忽视，直到20世纪90年代初。显然，现有的计算能力是太有限了，让这些方法有说服力的应用程序，但其他困难困扰的技术。时间序列数据通常是长期和颗粒有一种倾向，英年早逝。因此，该方法是由维度诅咒。但正如莎士比亚说，如果维咒诅，更好的算法useth。
原文：Ever wonder how the "Mars One" one-way trip to Mars will actually get to the planet without winding up on, say Venus? The tracking devices will use a nonlinear state space model. While inference for the linear Gaussian model is fairly simple, inference for nonlinear models can be difficult and often relies on derivative free numerical optimization techniques. A promising method that I will discuss is based on particle approximations of the conditional distribution of the hidden process given the data. This distribution is needed for both classical inference (e.g., Monte Carlo EM type algorithms) and Bayesian inference (e.g., Gibbs sampler).
Particle methods are an extension of sequential importance sampling (SIS). Although the SIS algorithm has been known since the early 1970s, its use in nonlinear problems remained largely unnoticed until the early 1990s. Obviously the available computational power was too limited to allow convincing applications of these methods, but other difficulties plagued the technique. Time series data are typically long and particles have a tendency to die young. Consequently, the approach is cursed by dimensionality. But as Shakespeare noted, if dimensionality curseth, a better algorithm useth.
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