Improving the Performance of Bayesian Estimation Methods in Estimations of Shift Point and Comparison With Maximum Likelihood Estimation Approach

A bayesian analysis is used to detect a change-point in a sequence of independent random variables from exponential distributions. 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 (mle) method is used for determining change point. the sensitivity analysis of bayes estimators are performed by simulation. also, we suggest a new approach to achieve more precise results by determining correct choice for parameters of prior distribution and compared the approach with existing methods. the result of simulation shows good performance of proposed approach in comparison with existing methods. also, a sensitivity analysis on the location of the shift is performed.