Dynamic exploration designs for graphical models using clustering with applications to petroleum exploration

The paper considers the problem of optimal sequential design for graphical models. Oil and gas exploration is the main application. Here, the outcomes at prospects or reservoir units are highly dependent on each other. The joint probability model for all node variables is considered known. As data is collected, this probability model is updated. The sequential design problem entails a dynamic selection of nodes for data collection, where the goal is to maximize utility, here defined via entropy or total expected profit. With a large number of nodes, the optimal solution to this selection problem is not tractable. An approximation based on a subdivision of the graph is considered. Within the small clusters the design problem can be solved exactly. The results on clusters are combined in a dynamic manner, to create sequential designs for the entire graph. The merging of clusters also gives upper bounds for the actual utility. Several synthetic models are studied, along with two real cases from the oil and gas industry. In these examples Bayesian networks or Markov random fields are used. The sequential model updating and data collection strategies provide useful guidelines to policy makers.