In this paper, we develop a practical and flexible framework for evaluating sequential exploration strategies in the case where the exploration prospects are dependent. Our interest in this problem was motivated by an oil exploration problem, and our approach begins with marginal assessments for each prospect (e.g., what is the probability that the well is wet?) and pairwise assessments of the dependence between prospects (e.g., what is the probability that both wells i and j are wet?). We then use information-theoretic methods to construct a full joint distribution for all outcomes from these marginal and pairwise assessments. This joint distribution is straightforward to calculate, has many nice properties, and appears to provide an accurate approximation for distributions likely to be encountered in practice. Given this joint probability distribution, we determine an optimal drilling strategy using an efficient dynamic programming model. We illustrate these techniques with an oil exploration example and study how dependence and risk aversion affect the optimal drilling strategies. The information-theory-based techniques for constructing joint distributions and dynamic programming model for determining optimal exploration strategies could be used together or separately in many other applications.

Strictly proper scoring rules continue to play an important role in probability assessment. Although many such rules have been developed, relatively little guidance exists as to which rule is the most appropriate. In this paper, we discuss two important properties of quadratic, spherical, and logarithmic scoring rules. From an ex post perspective, we compare their rank order properties and conclude that both quadratic and spherical scoring perform poorly in this regard, relative to logarithmic. Second, from an ex ante perspective, we demonstrate that in many situations, logarithmic scoring is the method least affected by a nonlinear utility function. These results suggest that logarithmic scoring is superior when rank order results are important and/or when the assessor has a nonlinear utility function. In addition to these results, and perhaps more important, we demonstrate that nonlinear utility induces relatively little deviation from the optimal assessment under an assumption of risk neutrality. These results provide both comfort and guidance to those who would like to use scoring rules as part of the assessment process.

No abstract

Discretization is a common decision analysis technique for which many methods are described in the literature and employed in practice. The accuracy of these methods is typically judged by how well they match the mean, variance, and possibly higher moments of the underlying continuous probability distribution. Previous authors have analyzed the accuracy of differing discretization methods across a limited set of distributions drawn from particular families (e.g., the bell-shaped beta distributions). In this paper, we extend this area of research by (i) using the Pearson distribution system to consider a wide range of distribution shapes and (ii) including common, but previously unexplored, discretization methods. In addition, we propose new three-point discretizations tailored to specific distribution types that improve upon existing methods.

An important task that petroleum engineers and geoscientists undertake is to produce decision-relevant information. Some of the most important decisions we make concern what type and what quality of information to produce. When decisions are fraught with geologic and market uncertainties, this information gathering may such forms as seismic surveys, core and well test analyses, reservoir simulations, market analyses, and price forecasts-which the industry spends billions of US dollars each year. Yet, considerably less time and resources are expended on assessing the profitability or value of this information. Why is that? This paper addresses how to make value-of-information (VOI) analysis more accessible and useful by discussing its past, present, and future. On the basis of a survey of SPE publications, we provide an overview of the use of VOI in the oil and gas industry, focusing on how the analysis was carried out and for which types of decisions VOI analysis has been performed. We highlight areas in which VOI methods have been used successfully and identify important challenges. We then identify and discuss the possible causes for the limited use of VOI methods and suggest ways to increase the use of this powerful analysis tool.