Oil exploration: sequential decisions in the face of uncertainty

A simple Bayesian model for oil exploration is suggested to investigate strategies for drilling. A condition on the way successes and failures affect the prior distribution implies a certain form of the detection mechanism. It is shown that the problem of finding strategies for drilling reduces to an optimal stopping problem. Two new families of distributions are obtained with generating functions related to classical work on partitions of integers. By using such distributions and simple mixtures of them as priors, the stopping problem can be solved explicitly. This leads to the construction of simple strategies and their effectiveness is demonstrated by evaluating suitable operating characteristics.