Abstract
We present a new approach for designing a sequential exploration program (Bickel and Smith, 2006) for selecting sites affected by spatial dependencies. Our motivation is the development of an oil field characterized by a complex system of prospect relations. The work exploits the Bayesian network model presented in Martinelli et al. (2011), where the nodes represent physical geological structures and the edges possible hydrocarbons' migration paths, with discrete outcomes {oil,gas,dry} at every node. The Bayesian network edges and associated probabilities are specified together with geological experts, and the resulting network model allows more flexibility than other spatial models. We use different heuristics for assessing the exploration strategies. The simplest strategy is a naive one drilling only wells with positive (marginal) expected revenues, while the (intractable) exact solution is given by dynamic programming; in between these two extremes, we propose a large range of possible approximations and we discuss the benefits and the tradeoff between accuracy and speed. We further show an application of the same methods to a more classical example of discrete spatial model, namely the Ising field, and we discuss the assumptions and approximations required to run a sequential decision program on large spatial models and the benefits of sequential strategies (Miller, 1975) versus once-only value of information based decision criteria (Bhattacharjya et al., 2010).