Abstract |
At a Superfund remediation site the decision is a classification problem, discriminating between polluted blocks to be remediated and background blocks to be left untreated. The concentration of the pollutant in a block is estimated from sampling. The more samples taken the better the estimates, but what is the optimum sample size. The errors are computed by subtracting the estimate from the block averages of an exhaustive sampling. The time-honored least squares algorithm is the obvious way to evaluate a given sample size, but least squares assumes a symmetric loss function. Superfund remediation has an asymmetric cost-plus-loss function; false positives (clean blocks judged dirty) have a relatively small fixed cost while false negative (polluted blocks judged clean) have public-health-losses that increase with concentration. Minimizing an asymmetric cost-plus-loss function will find a different optimum sample size than would the traditional least squares approach. |