Application of Bayesian Inference to Acceptance/Rejection Decisions On Offshore Lease Bids
Authors: Kaplan S. 
Published: December 2007

An approach is suggested for developing accept/reject criteria for offshore lease bids. The approach begins with the governments's knowledge of tract worth as expressed i a Monte Carlo-derived probability distribution. A Bayesian technique is used to update probability distribution. A Bayesian technique is used to update this distribution, and an accept/reject criterion based on the mean and the shape of the updated distribution is suggested.

Introduction
The results of the March 28, 1974, sale of leases off Louisiana contain some very interesting features. From these results the general rule the government seems to have applied in accepting or rejecting bids is simply to accept those bids that are higher than the Bureau of Land Management (BLM) estimated value and to reject those that are lower, even if only slightly lower. However, there are four exceptions to this rule in the data. In the case of Tracts 19, 155, 156, and 212, the high bids were accepted although they were considerably below the BLM estimated value.
These exceptions imply that the actual acceptance/ rejection criteria were more complicated than the simple rule. Information provided by the U.S. Dept. of the Interior reveals that, as part of their evaluation, they considered a parameter called "average evaluation of tract." This parameter is calculated by summing the value of all bids on a tract, adding the government's presale value, and dividing by the total number of bids presale value, and dividing by the total number of bids plus one. Thus, this parameter is an average of the plus one. Thus, this parameter is an average of the government's estimate with the bids received, and is intended as a measure of the "fair market value" of the tract. In all four tracts mentioned, the accepted high bid was substantially above this average evaluation of tract. What is interesting about the use of this parameter is that it implies recognition by the BLM of the difficulty of predicting tract valuation accurately and, in effect, amounts to a way of "updating" the BLM's own estimate in light of the estimates of the industry as reflected by the bids received.
If one accepts this idea of updating the BLM's estimate, it is interesting to ask whether there are ways other than taking a simple average to achieve this result. It is particularly interesting to ask whether it is possible to apply Bayes' theorem to this purpose, recognizing that Bayes' theorem is designed expressly for this kind of situation where there is an existing state of uncertainty and where new information is received and is to be incorporated.
Bayes' theorem may be applied very nicely to this updating problem. This paper calls attention to this application and suggests that it may serve as a basis for developing more satisfactory accept/reject criteria.
Since the approach presented here is totally couched in terms of probability theory, and since some subtleties arise in the use of this theory, the next section presents a concise statement of the point of view adopted here toward probability. Then, nomenclature is established relating to tract value and bidder's strategy. Bayes' theorem is presented, and the manner in which this theorem may be used to update estimates of tract worth, and thus, to guide accept/reject decisions, is formulated. Numerical examples based on the March 28, 1974, sale are included.

What Is Probability?
Pierre Simon de Laplace, one of the founders of Pierre Simon de Laplace, one of the founders of probability theory, said that probability is nothing but probability theory, said that probability is nothing but common sense reduced to calculation.
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