UPDATING UNCERTAINTY IN AN INTEGRATED RISK ASSESSMENT - CONCEPTUAL-FRAMEWORK AND METHODS

Bayesian methods are presented for updating the uncertainty in the pre dictions of an integrated Environmental Health Risk Assessment (EHRA) model. The methods allow the estimation of posterior uncertainty distr ibutions based on the observation of different model outputs along the chain of the linked assessment framework. Analytical equations are de rived for the case of the multiplicative lognormal risk model where th e sequential log outputs (log ambient concentration, log applied dose, log delivered dose, and log risk) are each normally distributed. Give n observations of a log output made with a normally distributed measur ement error, the posterior distributions of the log outputs remain nor mal, but with modified means and variances, and induced correlations b etween successive log outputs and log inputs. The analytical equations for forward and backward propagation of the updates are generally app licable to sums of normally distributed variables. The Bayesian Monte- Carlo (BMC) procedure is presented to provide an approximate, but more broadly applicable method for numerically updating uncertainty with c oncurrent backward and forward propagation. Illustrative examples, pre sented for the multiplicative lognormal model, demonstrate agreement b etween the analytical and BMC methods, and show how uncertainty update s can propagate through a linked EHRA. The Bayesian updating methods f acilitate the pooling of knowledge encoded in predictive models with t hat transmitted by research outcomes (e.g., field measurements), and t hereby support the practice of iterative risk assessment and value of information appraisals.