A Belief Network Approach to Optimization and Parameter Estimation in Resource and Environmental Management Models

This study presents an approach to use Bayesian belief networks in various optimization tasks in resource and environmental management. A belief network is constructed to work parallel to a deterministic model, and it is used to update conditional probabilities associated with different components of the model. The propagation of probabilistic information occurs in two directions in the network. The divergence between prior and posterior probability distributions at model components can be used as indication on inconsistency between model structure, parameter values, and other information used. An iteration scheme was developed to force prior and posterior distributions to become equal. This removes inconsistencies between different sources of information. The scheme can be used in different optimization tasks including parameter estimation and optimization between various management alternatives. Also multiobjective optimization is possible. The approach is illustrated with two numerical examples and with a hypothetical example on cost-effective management of river water quality.