Using power priors to improve the binomial test of water quality

• Published in: Journal of agricultural, biological, and environmental statistics Vol. 11; no. 2; pp. 151 - 168
• Main Authors: Duan, Y, Smith, E.P, Ye, K
• Format: Journal Article
• Language: English
• Published: Washington, DC American Statistical Association and the International Biometric Society 01.06.2006; American Statistical Association; International Biometric Society
• Subjects: Agronomy. Soil science and plant productions; Bayesion analysis; Binomials; Biological and medical sciences; Biometrics, statistics, experimental designs, modeling, agricultural computer applications; data collection; Datasets; Error rates; False negative errors; Frequentism; Fundamental and applied biological sciences. Psychology; Generalities. Biometrics, experimentation. Remote sensing; historical data; Power lines; Proportions; statistical analysis; Water quality; Water quality assessment; water quality standards; Water samples; Bayes estimation; Water quality standards; Historical data; Water quality standard; Water quality; Environmental monitoring; Case history; Bayesian analysis; Environment quality
• ISSN: 1085-7117; 1537-2693
• DOI: 10.1198/108571106X110919

To assess violations of water quality standards, measurements of water quality are collected on a regular basis over a period of time, and are then analyzed to evaluate the percentage of samples exceeding the standard. The challenge to the assessor is that often only a limited amount of data are used to determine if the stream is violating standards. Current assessment uses just the data for a period of two years. To address this issue, we present a Bayesian approach using power priors to incorporate historical information in decision-making. We demonstrate a modified power prior approach and discuss its properties under a binomial model. Exact error probabilities are compared using three approaches: a power prior approach to the binomial test, a Bayesian binomial test with noninformative prior, and a frequentist binomial test. Two examples are presented to illustrate the implementation of the power prior and its differences with alternative binary methods in water quality assessment.