Comparison of a Bayesian and a standard approach for estimating a temporal trend of perfluoroalkyl acids in sewage sludge

ABSTRACT

A comparison of two alternative approaches is presented, which are used to assess on a regional scale a dominating temporal trend of concentrations of long-chain perfluoroalkyl acids (PFAAs) in sewage sludge. The question is tackled whether a dominating trend can be deduced from a few actual determinations, as few as possible. This study uses time series of concentrations of PFAAs in sewage sludge, represented by regression slopes from 729 waste water treatment plants. The standard approach for assessing a dominating trend is based on arithmetic means, standard deviation and standard error. The alternative approach is based on Bayesian parameter estimation. Both approaches are compared within a Monte Carlo sampling. With the standard approach, at least 40 regression slopes are necessary to reduce the standard error to a reasonable degree, even by including 60 regression slopes the standard deviation does not level off. The Bayesian approach achieves trustworthy results with fewer data: by including 21 regression slopes into the evaluation, the probability already exceeds 90% for estimating the same temporal trend as if all 729 regression slopes would have been evaluated.

KEYWORDS:

• Bayesian parameter estimation
• perfluoroalkyl acids
• Monte Carlo simulation
• temporal trend
• sewage sludge

Acknowledgments

We thank Thomas Meierfels and Arnold Rupprich for providing the data for this study. We cordially thank our supervisor Michael Gierig for supporting the idea of testing a Bayesian approach for data evaluation. Great thanks go to two anonymous reviewers and Hartmut Frank, Nivedita Mahida-Königsdörfer and Marion Letzel whose comments and suggestions helped to improve this manuscript in structure, conciseness and language.

Disclosure statement

No potential conflict of interest was reported by the authors.