Improving the Performance of Bayesian Estimation Methods in Estimations of Shift Point and Comparison with MLE Approach

A Bayesian analysis is used to detect a change-point in a sequence of independent random variables from exponential distributions. In This paper, we try to estimate change point which occurs in any sequence of independent exponential observations. The Bayes estimators are derived for change point, the rate of exponential distribution before shift and the rate of exponential distribution after shift. Likelihood, Prior, Posterior and Marginal distribution of the change point is derived. Also maximum likelihood estimation method is used for determining change point. The sensitivity analysis of Bayes estimators are performed by simulation. Also we suggested a new approach to achieve more precise results by determining correct choice for parameters of prior distribution and compared new approach with existing methods. The result of simulation shows good performance of proposed approach in comparison with existing methods