Rules of decision-making about the variance of a Gaussian distribution are obtained and compared. Considering the square error loss function, an approximate Bayesian decision rule for the variance of a normal population is derived. Using normal data and SAS software, the obtained approximate Bayesian test results were compared to their counterparts obtained with the well-known classical decision rule. It is shown that the proposed approximate Bayesian decision rule relies only on observations. The classical decision rule, which uses the Chi-square statistic, does not always yield the best results: the proposed approach often performs better.
Camara, Vincent A. R.
"A New Approximate Bayesian Approach for Decision Making About the Variance of a Gaussian Distribution Versus the Classical Approach,"
Journal of Modern Applied Statistical Methods:
1, Article 22.
Available at: http://digitalcommons.wayne.edu/jmasm/vol8/iss1/22