The Parameter Estimation Of The Statistics Models Based On The MCMC Method

The MCMC method is one of the most important algorithms in the modern statistical calculations. This algorithm provides a useful tool for realistic statistical modeling, and has become very popular for Bayesian computation in complex statistical models. The two usual sampling methods in MCMC are the Gibbs sampler and the M-H Strategies.In this paper, by using the random walk Metropolis-Hastings strategies in the MCMC method, with a bivariate normal proposal we first estimate the parameters of the trinomial Logit model, and give the proof of the conditions, the design of algorithms and the MC simulations. We estimate the parameters of the trinomial Logit model that has a regression vector and present the simulation results of the algorithms. Meanwhile, we estimate the Logit model with real data from the early warning system of foreign exchange risk, actualizing the early warning for the system of foreign exchange. Secondly, by using the MCMC method we estimate the Probit model and present the simulations for related algorithms. Finally, by using the Gibbs sampler and the Adaptive rejection sampling in the MCMC method, we estimate the parameters of the inverse gamma distribution directly. The results show a good and flexible behavior of this method for estimating the true values of parameters compared to the traditional method like MLE. This method can also be used in other more complex models, such as, the nested Logit model and the multinomial Probit model and so on.