Study on Stochastic Simulation of the Bayesian Dynamic Models

Abstract: The problems about parameter estimation and the selection of model in Bayesian Dynamic Model have not been solved successfully. According to the success of stochastic simulation method (also called Monte Carlo method) when it is used in the integral of high dimension or modeling, we use the Monte Carlo method to resolve the parameter estimation problems and the selection of the model in Bayesian Dynamic Model and achieved some good results.It is difficult to estimate the parameters of nonlinear Bayesian Dynamic Model directly. While the mixed model with finite element provides us a method for fitting a complicated probability density function with a simple structure and estimate the parameters. In section 3, we use MCMC simulation method to estimate the parameters of the mixed model and make an improvement in this way. During the process of MCMC simulation, the convergence rate of the Markov chain is extremely important for forecasting. To get a fast convergence, we present a modified MCMC method for nonlinear state space model in section 4, which we call the Embedded Hidden Markov Model (EHMM) sampling method. The convergence rate of this method is much faster than the traditional MCMC method. We prove the result and illustrate it with an example of 1-dimensional nonlinear space.During the selection of Bayesian Dynamic model, two models can not be transferred to each other reversibly if they are of different dimensions. To make the transference reversible, we develop a reversible jump sampling structure which obeys the Metropolis-Hasting rule in section 5. In addition, to realize the selection and control of model we need to calculate the Bayes factor. To do this, Newton and Raftery put it out with an modified average estimation. Lewis and Raftery gave a Laplace Metropolis Estimator. But in both of the methods, the regular constant is difficult to get. In this essay, we calculate the Bayesian factor with the Path Sampling method which was obtained by Gelman and Meng, which made the calculation of Bayes factor very easy…
Key words: Bayesian Dynamic Model; stochastic simulation; MCMC simulation; EHMM Sampling; Path Sampling; reversible jump sampling

This entry was posted in Master Thesis. Bookmark the permalink.