In the first stages of formulating decision strategies, risk estimates may have to be based on sketchy information and limited experience. It is often important to be able to revise, or improve, the original risk estimates as new information becomes available. This is where Bayesian analysis comes in. Introduction In recent years there has been a great deal of emphasis on the use of expected-value concepts in the analysis of decisions under uncertainty. Expected values are risk-adjusted criteria that can be used by the decision maker to compare and select capital investment projects. A significant aspect of expected value criteria is that they provide a means to express the degree of risk and uncertainty in quantitative terms. These quantitative risk statements (or estimates) are the probabilities of occurrence of the various possible outcomes of a decision choice. As one might suspect, the probability numbers, or risk estimates, are critical factors in the expected value analysis of decisions involving risk and uncertainty. Frequently we must analyze decision choices in situations where there is very little information or experience upon which to base the risk estimates. Although these probabilities may be only approximate, they presumably represent the best estimates of risk at the time of presumably represent the best estimates of risk at the time of decision making and must be used to formulate initial decision strategies. It is often important to be able to revise, or improve, the original risk estimates as new information becomes available. This is where Bayesian analysis comes in. The purpose of this paper is to explain the logic and philosophy of Bayesian analysis - a formalized, statistical method philosophy of Bayesian analysis - a formalized, statistical method of updating risk analysis. First we shall consider Bayes' theorem and the mechanics of Bayesian computations. Then we shall discuss how Bayesian analysis is used in situations involving a series of new information - that is, in sequential sampling. Finally, we shall discuss the key issues of both sides of the controversy that surrounds the use of Bayesian analysis in business decisions. The Decision-Making Process - An Overview The decision-making process is actually a series of steps, or phases. Enumeration of these steps makes clearer the role of phases. Enumeration of these steps makes clearer the role of Bayesian analysis:Define the possible outcomes (states of nature) and the decision choices available to the decision maker.Associate the probabilities of occurrence and economic considerations with each of the possible outcomes.Select investment strategy, based on expected-value criteria.Note the results (outcomes) of the initial choice.Revise the risk estimates using Bayesian analysis and whatever information stems from Step 4.Modify the investment strategy, if necessary, on the basis of new expected-value analysis and revised risk estimates. The first three steps are basic to the initial quantitative analysis of any investment decision involving uncertainty. The remaining steps represent a "monitoring system" to provide the basis for managerial decisions regarding changes in investment strategies with time. JPT P. 193
Many important random variables in drilling-prospect analysis are dependent. A realistic appraisal of risk and uncertainty must recognize such dependency relationships. This paper discusses how to determine if random variables are dependent and how to modify the normal sampling procedures on each simulation pass to account for observed partial procedures on each simulation pass to account for observed partial dependencies. Introduction Over the past few years there have been many publications on the use of Monte Carlo simulation publications on the use of Monte Carlo simulation methods for analyzing risk and uncertainty. Most explain how to describe a distribution for each random variable and then sample a value from each distribution for each pass using a random number as the entry point in a pass using a random number as the entry point in a cumulative frequency distribution of the variables. Many analysts fail to realize that this procedure implies that each random variable is independent of all others. In reality, certain important random variables in drilling-prospect analysis are dependent, and a realistic appraisal of risk and uncertainty must recognize such dependency relationships. An obvious example is netpay thickness and initial potential. Both are random variables because we do not know their exact values before the well is drilled; and we normally choose to define the uncertainties associated with net pay and initial potential as probability distributions. But we also know that thickness and productivity are related by means of Darcy's equation. The question, then, is how do we adjust our sampling scheme on each pass so as to be able to sample values for both variables - but in a manner that honors the known dependency that exists between them? This paper discusses two important issues relating to random-variable dependencies:how to determine if two or more random variables are dependent; andhow to modify the normal sampling procedures on each simulation pass to account for observed partial dependencies between random variables. How To Determine if Random Variables Are Dependent There are various statistical measures of correlation (or the lack of correlation) that can be used to determine whether two or more random variables are statistically dependent on one another. But an easier way that eliminates a lot of statistical theory is to make a cross-plot of the available numerical data of the two variables of concern. For example, if we had thickness and initial-potential data from a series of wells (or fields) and wished to determine if a dependency relationship existed, we could plot thickness on one axis and initial potential on the second axis on coordinate graph paper. Each plotting point would correspond to the thickness/potential data of point would correspond to the thickness/potential data of one well (or field). Observing how the plotted data are arranged provides important insights about possible dependencies. For example, suppose we had numerical data of two random variables, A and B, and made a cross-plot to determine if any dependency relationships existed, as shown in Fig. 1. What would we conclude about any possible dependencies? We could probably agree that possible dependencies? We could probably agree that there appears to be no dependency. High values of A occur with low values of B and vice versa. JPT P. 1145
This paper proposes five risk analysis models for analyzing drilling prospects. The models range from a simple, two-outcome analysis (Levell) to a full Monte Carlo simulation risk model (Level 5) that takes into account all geologic and economic uncertainties.The five levels offer an orderly plan for implementing risk analysis techniques in drilling prospect evaluations. Explorationists can enter the progression at any point, and then gradually expand and enlarge the scope of their evaluation model by following the stepwise progression.
d method of assessing and describing the degree of uncertainty involved in the dedication of capital for drilling an oil or gas well is presented. The problem involves associating probabilities with the range of profitabilities that might result from a particular drilling prospect.This method of risk analysis recognizes the probabilistic nature of the variables affecting profitability. The method systematically combines the distributions of each variable into a final distribution of ultimate profitability. The entire range and distribution of financial outcomes that might occur from the drilling of the prospect and their related probabilities of occurrenCe are provided. A numerical example is given t~illustrate the use of the method.
American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. This paper was prepared for the 43rd Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Tex., Sept. 29-Oct. 2, 1968. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract This paper discusses utility theory and the corollary notion of expected utility as a decision criterion for drilling investments. The nature and historical background of utility theory are described. It is shown that expected utility is a logical extension of mathematical expectation. Expected utility has the distinct advantage [compared with expected monetary value and other well known measures of investment worth] of quantitatively treating certain preferences and biases of the decision maker. A numerical example is included to illustrate how utility theory can be incorporated into drilling investment evaluations. One problem in implementing utility theory has been the lack of suitable methods of constructing the function [utility curve] which describes the decision maker's preferences for monetary profits and losses. Past research efforts on this problem are summarized. In a recent university research project, a new method of constructing utility curves was developed and is briefly reviewed. This new method appears adequate to permit an attempt to implement utility theory on a trial basis. Suggestions for such a trial are given. Introduction The decision process in which corporate funds are allocated to specific exploratory and development well investment opportunities consists of two sequential steps. Initially, the petroleum explorationist considers the probable geologic conditions that might occur probable geologic conditions that might occur at the proposed location. These conditions are translated to financial profits [or losses], and if the location appears to offer some degree of profit potential, it is submitted to management. This portion of the decision process is usually performed by the professional process is usually performed by the professional staff and might be called the "predictive phase". phase".After the prospect has been presented to the decision maker, he must associate some measure of value to the probable financial outcomes and evaluate how these measures of value relate to the current goals and policies of the firm. This final step involving management personnel might be called the "value phase" of personnel might be called the "value phase" of the decision process. This paper will be concerned with the value phase of exploratory and development well decision processes. The decision maker's reactions to the probable financial outcomes of a prospect are probable financial outcomes of a prospect are influenced by such factors as the firm's current asset position, corporate goals, and his preferences regarding risk. Certainly, these preferences regarding risk. Certainly, these and other factors are considered in every drilling investment decision.
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