Model parameter uncertainty estimation based on Bayesian inference for activated sludge model under aerobic conditions: a comparison with a linear theory method

The purpose of the study is to apply Bayesian inference in order to estimate the uncertainty in model parameters and predictions for environmental models. The analysis was based on a global optimization routine that finds good initial values for an adaptive Markov chains Monte Carlo (MCMC) algorithm that finally computes the posterior parameter distribution. A revised activated sludge model was used in order to perform a comparison between Bayesian and linear theory methods. It was observed that the linear theory method systematically underestimates the confidence intervals of the estimated model parameters because the multivariate normality assumption is violated and practical unidentifiability for some parameters occurs