Evaluating water quality using power priors to incorporate historical information

Abstract

To assess water quality standards, measurements of water quality under the Clean Water Act are collected on a regular basis over a period of time. The data are analyzed to evaluate the percentage of samples exceeding the standard. One problem is that current data are limited by the time range and consequently the sample size is inadequate to provide necessary precision in parameter estimation. To address this issue, we present a Bayesian approach using a power prior to incorporate historical data and/or the data collected at adjacent stations. We develop a modified power prior approach and discuss its properties under the normal mean model. Several sets of water quality data are studied to illustrate the implementation of the power prior approach and its differences from alternative methods. Copyright © 2005 John Wiley & Sons, Ltd.