Approximate Bayesian Confidence Intervals for The Mean of a Gaussian Distribution Versus Bayesian Models

Abstract

This study obtained and compared confidence intervals for the mean of a Gaussian distribution. Considering the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for the mean of a normal population are derived. Using normal data and SAS software, the obtained approximate Bayesian confidence intervals were compared to a published Bayesian model. Whereas the published Bayesian method is sensitive to the choice of the hyper-parameters and does not always yield the best confidence intervals, it is shown that the proposed approximate Bayesian approach relies only on the observations and often performs better.