Regression Model And The Weibull Distribution Change Point Problem Of Bayes Estimation

In this paper, we use Bayesian method to discuss the change point problem of quadratic linear regression models and Weibull distributions with the number of the change points known.In Chapter 2, we solve the problem of quadratic linear regression model with one, two or more than two change points. The change points are due to the change in the regression coefficients or in both the regression coefficients and variance. In the method, we give the posterior distributions and the Bayesian estimates of the parameters by use of the property of the X~2 distribution and t distribution. As a result, the posterior distributions of the regression cofficients are mixtures of t distribution, while a mixture of inverse gamma distributions is the posterior distribution of variance. MSEs of some Bayesian estimates are compared by Monte Carlo methods with those of the MLE. The MSE of the Bayesian estimates of the change point is uniformly smaller than those of the MLE, while the MSEs of the Bayesian estimates of the regression cofficients are also smaller than those of MLE.In Chapter 3, we discuss the change point problem of Weibull distributions using Bayesian method. The change of shape paramter and scale paramter cause the change of weibull distribution. We use Gibbs Sampling (Adaptive Rejection Sampling ) and the method of Laplace, and obtain the Bayesian estimates of the parameters of the distribution and the change points.