AbstractContaminant concentration data collected at Superfund sites are typically positively skewed, and the log‐normal distribution is commonly used to model such data distribution. U.S. EPA guidance documents recommend the use of H‐statistics to compute the upper confidence limit (UCL) of the mean of a log‐normal distribution. Recent work reported in the statistical literature has shown that the UCL calculated from the H‐statistics can yield extremely high false positives. In the present article we compute the Bayesian highest posterior density (HPD) credible set of the log‐normal mean. Simulated results using techniques of computational geometry are presented. Several experimental results on environmental data sets reveal that the UCL obtained by using the proposed Bayesian approach is more reasonable than those obtained by using other techniques. Copyright © 2002 John Wiley & Sons, Ltd.