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# Bayesian stochastic simulation of dynamic models

Author: BaoYunXia
Tutor: LiuFuSheng
School: Shandong University of Science and Technology
Course: Applied Mathematics
Keywords: Bayesian dynamic model Stochastic Simulation MCMC simulation Mixed model approach EHMM sampling Reversible jump Path sampling method
CLC: O212.8
Type: Master's thesis
Year: 2005
Downloads: 506
Quote: 3
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### Abstract

 Bayesian theory of dynamic model parameter estimation and model selection problems have yet to find a good solution , while the stochastic simulation method ( also known as the Monte Carlo method ) in solving high-dimensional probability density integration issues and statistical modeling and inference made the success inspired us to apply this method to solve Bayesian dynamic model parameter estimation and model selection problems . This paper to try and get some results. Directly to the nonlinear dynamic model of Bayesian parameter estimation is quite difficult, and finite mixture model provides a simple structure with complex probability density fitting method , therefore, in the third chapter , we will first nonlinear Bayeux Adams dynamic model into finite mixture model , and then use the Markov chain Monte Carlo (MCMC) simulation Gibbs sampling method to estimate the mixing parameters in the model in order to achieve the improvement of the parameter estimation problem . In MCMC simulation process , Markov chain convergence rate is crucial for the effect predicted by the model , in order to improve the convergence speed, we used in Chapter embedded hidden Markov model (EHMM) sampling method to construct a Markov chain . Can be proved that the method converges faster than the traditional method of MCMC convergence rate has accelerated noticeably. It is proved that this conclusion and one -dimensional nonlinear state space model as an example to illustrate this. Dynamic Bayesian model selection process, when the two dimensions of state parameters of the model is not the same , the transfer between them is irreversible , in order to overcome this difficulty, we are in the fifth chapter of guidelines designed by Metropolis-Hasting reversible jump samplers , and thus achieve a different dimension reversible jump between models . Factor in the use of Bayesian model selection and monitoring , the Bayes factor for the calculation of how the problems , Newton and Raftery proposed using the modified harmonic mean to estimate , Lewis and Raftery proposed Laplace-Metropolis estimation methods, but this Both methods Regularization constant calculation problem is very complicated . In this paper, Gelman and Meng proposed path sampling method (Path Sampling) to calculate the Bayes factor , very simplified regularization constant calculation .

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Mathematical Statistics > Bayesian statistics
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