Statistical decision theory is the mathematical analysis of decision problems in which uncertainty is a key element. Use of it can give the oil and gas operator ordered insight into the way exploration decisions should be made in order to achieve preassigned goals; e.g., maximize the net expected present value of an exploratory drilling program. It does this by forcing the decision-maker to make explicit assumptions and judgements that are implicit in every such decision problem. In other words, statistical decision theory is a vehicle for rendering precise the key variables and relations among them that constitute the core of exploration problems. It is important to recognize, however, that people-not mathematical models-make decisions, so statistical decision theory is only an aid to decision-making, not a decision-making device.

Rather than emphasize the specifics of how statistical decision theory comes into play in analysis of exploration problems, in this paper we will concentrate on illustrating how statistical methodology can be used to build a probabilistic cornerstone of mathematical models of some important exploration decision problems.

As pointed out in Ref. 1, in any decision concerned with the strategy and tactics of oil and gas exploration, a key variable is the size of hydrocarbon deposits in barrels of oil or in Mcf of gas. The size of pool or field discovered in a particular wildcat venture determines the degree to which the venture is an economic success. Since the pool or field size that will be discovered is almost always unknown before a prospect is drilled, an important question is: "What functional form of distribution function should be used to characterize the probability distribution of field sizes in a petroleum province?" By "functional form" we mean a mathematical formula which defines a family of distribution functions.

Clearly, the functional form used to characterize the size distribution of oil and gas fields is a vital part of any model which you as decision makers might use to analyze exploration decisions. Ideally, we would like this form to be flexible enough to fit a wide variety of empirical histograms of oil and gas fields in differing areas with differing definitions of reserves by varying only the value of the parameters of the form, not the form itself. We also would like it to be analytically tractable, so that it may be easily used in the course of a formal analysis of exploration decision problems; e.g., by use of statistical decision models. The Lognormal functional form has these properties,

It may be shown to be in concordance with some concepts of how mineral deposits are formed.

Stochastic models of the discovery process built on reasonable assumptions about the process lead to the Lognormal functional form.

The class of lognormal functional forms is analytically tractable and flexible enough to capture most reasonable oilmen's subjective betting odds about random variables such as reported field size.

A detailed discussion of these points, a development of several methods for blending subjectives probability beliefs of experts about field sizes that are not known with certainty with objective evidence, and application of these methods to some typical exploration decision problems - notably drilling decision problems—are given in Refs. 1 and 2. Both references show how concepts from statistical decision theory can be used to analyze such problems.

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