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In this book, we studied the model selection and its parameter estimation through Bayesian techniques, In Applied Decision Theory, usually we consider Bayesian Analysis and Estimation Theory, a Bayes Estimator is an estimator or decision rule that maximizes the posterior expected value of a utility function or minimizes the posterior expected value of a loss function. The Bayesian Estimation of parameter in the case of Shift or Change Point in Poisson Sequence, Gamma Sequence and in Pareto Sequence under Squared Error Loss Function(SELF), LINEX Loss Function(LLF) and Precautionary Loss Function(PLF) and General Entropy Loss Function(GELF) was carried out and the comparisons are made among the different loss functions in the Poisson Sequence and Pareto Sequence within. The observed data like life time data, economic data, industrial data etc; can be consider in which there may be a sudden change or failure in life test will occur, It is very important to know when and where a change will occur and the Bayesian estimation of its parameter will be calculated and the inference will be drawn which is very important to take decision regarding the shift point in the life testing models.