ABSTRACT

Bayesian methods have been developed to analyze three main types of uncertainties, namely: the model uncertainty, the parameter uncertainty, and the sampling errors. To illustrate these techniques on a real case study, a model has been developed to quantify the various uncertainties when predicting the global proportion of coliform positive samples (CPS) in a water distribution system where bacterial pollution indicators are weekly monitored by sanitation authorities. The data used to fit and validate the model correspond to water samples gathered in the suburb of Paris. The model uncertainty has been evaluated in the reference class of generalized linear multivariate autoregressive models. The model parameter distributions are determined using the Metropolis-Hastings algorithm, one of the Monte Carlo Markov Chain methods. Such an approach, successful when dealing with water quality control, should also be very powerful for rare events modeling in hydrology or in other fields such as ecology.

INTRODUCTION

The bacterial pollution indicators are understood here as the coliforms, a group of bacteria that is “public enemy number one” for water suppliers. Their occurrence in domestic distributed waters is a major concern for many utility companies. The coliform group includes many different species, the most famous one being Escherichia coli. Part of the bacteria belonging to the coliforms group are fecal bacteria and may provoke gastroenteritis or other digestive problems. The other inoffensive part is generally considered as an indicator of a possible presence of their more dangerous cousins.