David Stoffer 教授在廈門大學(xué)統(tǒng)計(jì)學(xué)進(jìn)行了一場主題為非線性狀態(tài)空間模型的講座，在職研究生講座的主要內(nèi)容如下：

　　有沒有想過如何在“火星一號(hào)”單程火星之旅將實(shí)際獲得的行星，那里沒有清盤時(shí)，說金星?跟蹤設(shè)備將使用非線性狀態(tài)空間模型。雖然推斷線性高斯模型是相當(dāng)簡單的，推理的非線性模型是很困難的，往往依賴于衍生自由數(shù)值優(yōu)化方法。一個(gè)有前途的方法，我將討論的基礎(chǔ)上給出的數(shù)據(jù)隱藏進(jìn)程的條件分布的顆粒近似。因?yàn)閮烧咝枰�的古典推理這種分配(例如，蒙特卡洛EM型算法)和貝葉斯推理(例如，吉布斯采樣)。

　　粒子的方法是連續(xù)重要性采樣(SIS)的延伸。雖然SIS算法已自20世紀(jì)70年代初稱，其在非線性問題的使用仍然在很大程度上被忽視，直到20世紀(jì)90年代初。顯然，現(xiàn)有的計(jì)算能力是太有限了，讓這些方法有說服力的應(yīng)用程序，但其他困難困擾的技術(shù)。時(shí)間序列數(shù)據(jù)通常是長期和顆粒有一種傾向，英年早逝。因此，該方法是由維度詛咒。但正如莎士比亞說，如果維咒詛，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.