| 讲座简介： | ABSTRACT: 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. |
