A Bayesian observation error model to predict cyanobacterial biovolume from spring total phosphorus in Lake Mendota, Wisconsin

We developed a logistic model for predicting summer blue-green biovolume from mean (log metric) spring total phosphorus concentration in Lake Mendota, Wisconsin. The model incorporates uncertainty in the sample estimates of the ''true'' mean total phosphorus values. We used Bayes Theorem to assess model parameters and predictive uncertainty from 19 years of data. When compared with a ''naive'' model that does not accommodate phosphorus uncertainty, the observation error model has a higher parameter variance, but lower prediction uncertainty. Lower prediction uncertainty occurs because some of the noise in the data is resolved as phosphorus uncertainty, thus reducing the variance of the model disturbance term. The observation error model results in less stringent phosphorus targets to meet acceptable blue-green levels than does the naive model because of this lower prediction uncertainty.