A Note on Prior Selection in Bayesian Estimation

Abstract

The parameter according to the Bayesian approach is handled as a variable that is random and with a probability distribution, rather than an unknown and fixed number. Statistical inference is dependent on the posterior distribution of the parameter rather than only the likelihood function. Choosing the prior distribution is a fundamental step in determining the posterior distribution, and it can be done objectively or subjectively. When the subjective technique is utilized, the prior distribution reflects the prior information the researcher had before coming into contact with the data. When utilizing the objective method, the prior distribution can be chosen in such a way that it has the least influence on the prior distribution. In this paper, a new way of selecting the prior distribution in Bayesian analysis was proposed. According to this strategy, for a given distribution, the prior distribution should be comparable to or the same as the data distributed. The performance of this method was compared to other estimation methods and found to have significantly better performance compared to other estimators. This result was confirmed though a Monte Carlo simulation experiments, with some selected performance criteria mainly, the root mean squared error (RMSE) and the Bias.