Characterizing Variability and Uncertainty in Data Sets Using Bootstrap Simulation. H. Christopher Frey, Department of Civil Engineering, North Carolina State University, Raleigh, NC 27695-7908
Variability arises due to differences in the value of a quantity among different members of a population. Uncertainty arises due to lack of knowledge regarding the true value of a quantity for a given member of a population. We evaluate the use of bootstrap simulation for quantifying both variability and uncertainty in the form of uncertain frequency distributions. The source of uncertainty addressed here is random sampling error. Bootstrap simulation is applied to three data sets to illustrate the use of the method and the insights that it provides. The data sets include a synthetic sample of 19 values from a lognormal distribution, a sample of 9 values obtained from measurements of the PCB concentration in leafy produce, and a sample of 5 values obtained regarding the partitioning of chromium in the flue gas desulfurization system of coal-fired power plants. For each data set, bootstrap simulation is used to characterize uncertainty in the arithmetic mean and standard deviation, the parameters of the distributions, cumulative distribution functions based upon fitted parametric distributions, the 95th percentile of variability, and the 63rd percentile of uncertainty for the 81st percentile of variability. We compare characterizations of uncertain frequency distributions based upon different methods for fitting distributions for variability to data, including the method of matching moments and the method of maximum likelihood. Our results indicate that with only 5 to 19 data points as in the data sets we have evaluated, there is substantial uncertainty Bootstrap simulation is applied to three data sets to illustrate the use of the method and the insights that it . . . . . . [RiskWorld Note: Submitted abstract incomplete]