Abstract: We discuss some questions on the Bayesian Dynamic Models in this article. First, some random simulations are introduced and the important sample is improved, which supplies the method and theory for the choice of the important sample. My main work is applying the particle filter algorithm to random simulate the non-linear Bayesian dynamic models. The particle filter algorithm is suitable for the non-linear and nonnormal restraint based on the simulative statistical filter algorithm. Using it we can approximately obtain the expectation of any function, using the certain quantity the random sample particle to express the posterior density of random variable in the model, and can be used in the any non-linear random models. We discussed the application of the particle filter algorithm and its improved algorithm in the non-linear dynamic model forecast in the article. A kind of Bayesian dynamic model with nonlinear state equation is solved by Tierney and Kadane' s approximate computation. This article is divided into five parts total. The first part is introduction; the Second part reviewed Bayesian dynamic model and its forecast theory; the third part discussed the application of the particle filter in Bayesian dynamic model forecast; This part also discussed Kalman Filter algorithm and Grid-Based Methods. At the same time discussed applying the extended Kalman filter, approximate grid-based methods, particle filters which were used to solve non-linear problem to approach the ideal Bayesian's theory. The fourth part discussed the application of the improved particle filter in non-linear dynamic models; Brought forward several new algorithms to realize the forecast. Finally we mainly discussed the Tierney and Kadane' s approximate computation in a kind of non-linear dynamic model…

Key words: the nonlinear Bayesian Dynamic Models; random simulation; the particle filter algorithm; the Kalman filter; the important sample; the Tierney and Kadaneâ€™ s approximate

# Application of Particle Filter in the Bayesian Dynamic Models

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