ABSTRACT
Risk analysis and estimation techniques The problem considered in this chapter is that of estimating the nature of the size distribution of petroleum reservoirs and their values.
The method used consists of a Bayesian technique for parameter estimation. A sampling procedure based on minimizing the mean square error (MSE) of the posterior Bayesian estimator is developed using the beta density function to model the prior distribution. This Bayesian approach provides several typical representative distributions which are broad enough in scope, to provide a satisfactory economic analysis. These distributions re¤ect general patterns of similar regions, and include dry holes, as well as several representative class sizes of discoveries, and of course the probabilities associated with each of these classes. Mathematical expressions are provided for the probability estimates for the three-category case, as well as for the general case of k samples. This Bayesian method permits a more detailed economic analysis than is possible by the use of binomial distribution, where wells are simply classi‰ed as good or bad.
