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Oil exploration: sequential decisions in the face of uncertainty

Published online by Cambridge University Press:  14 July 2016

L. Benkherouf  and
J. A. Bather
L. Benkherouf*
Affiliation:
Imperial College
J. A. Bather*
Affiliation:
University of Sussex
*
∗ Postal address: Imperial College of Science and Technology, Department of Mathematics, Queen's Gate, London SW7 2BZ, UK.
∗∗ Postal address: School of Mathematical and Physical Sciences, The University of Sussex, Falmer, Brighton BN1 9QH, UK.
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Abstract

A simple Bayesian model for oil exploration is suggested to investigate strategies for drilling. A condition on the way successes and failures affect the prior distribution implies a certain form of the detection mechanism. It is shown that the problem of finding strategies for drilling reduces to an optimal stopping problem. Two new families of distributions are obtained with generating functions related to classical work on partitions of integers. By using such distributions and simple mixtures of them as priors, the stopping problem can be solved explicitly. This leads to the construction of simple strategies and their effectiveness is demonstrated by evaluating suitable operating characteristics.

Keywords

SEARCH MODELOPTIMAL STOPPINGORDERING PRIOR DISTRIBUTIONSEULER'S IDENTITYPARTITIONS OF INTEGERS
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 3 , September 1988 , pp. 529 - 543
Copyright
Copyright © Applied Probability Trust 1988 

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References

Andrews, G. E. (1976) The theory of partitions. Encyclopedia of Mathematics and its Applications, 2. Addison-Wesley, Reading, Massachusetts.Google Scholar
Beale, E. M. L. (1986) Optimization methods in oil and gas exploration. IMA J. Appl. Math. 36, 1–10.Google Scholar
Whitt, W. (1979) A note on the influence of the sample on the posterior distribution. J. Amer. Statist. Assoc. 74, 424–426.Google Scholar