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.
Camara, Vincent A. R.
"Approximate Bayesian Confidence Intervals for The Mean of a Gaussian Distribution Versus Bayesian Models,"
Journal of Modern Applied Statistical Methods:
2, Article 17.
Available at: http://digitalcommons.wayne.edu/jmasm/vol8/iss2/17