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Abstract
Sound decision making requires the elicitation and quantification of key
uncertainties. Probabilities are, in general, subjective and most
petro-technical experts find assessing them challenging. Furthermore, much
evidence shows that, although they may not be aware of it, assessors find it
difficult to make unbiased assessments.
We show how the maximum entropy principle, an idea from information theory, can
be used to overcome the challenge of uncertainty assessment in oil & gas
decision-making situations. It has found great popularity in natural language
processing, space communication, biomedical engineering, and many other fields
but has received limited attention in oil & gas. After describing how the
technique can be adapted to information typical of oil and gas, we illustrate
its application to a field development decision.
We conclude that the maximum entropy approach can incorporate many types of
partial information. The examples and applications in this paper illustrate the
relevance and power of the approach for quantifying probabilities in the
context of oil E&P decision making. It is shown that arbitrarily
“interpolating” between assessed probabilities, or ignoring dependencies, can
lead to biased probability distribution, which in turn may lead to sub-optimal
decisions.
Introduction
Probability quantification has two main components. The first is the definition
of the possible outcomes of an uncertain event (or quantity), and the second is
the assignment of probabilities to those outcomes. The process of obtaining
this information is called elicitation.
Although subjective probability assessment is the dominant way to quantify
uncertainty, decision makers and petro-technical professionals often find these
assignments challenging. First, limited knowledge, combined with the number and
complexity of the probabilities, can be overwhelming. Dependence between the
uncertainties (which is often present) requires the assessment of correlations
or of joint or conditional probabilities, exacerbating the difficulty. Second,
much evidence shows that, although they may not be aware of it, assessors find
it difficult to make unbiased assessments (see, for example Tversky &
Kahneman, 1974; Morgan & Henrion, 1990; Capen (1976); Welsh et al (2004,
2005, 2007a, 2007b, 2007c).
A decision situation may have a single key uncertainty or a set of
uncertainties, which may be independent or dependent. The single-uncertainty
situation requires that the expert assess the marginal probabilities for the
possible outcomes, whilst the situation with several uncertainties may require
the expert to also assess conditional or joint probabilities. Assessing these
probabilities may not be easy, and the number of assessments needed for a joint
distribution of N variables, each discretized to k outcomes, is of the order
kN. Often the expert is unable to specify fully the relevant probability
distributions, necessitating a methodology that can be used to derive the fully
specified distributions whilst being consistent with whatever partial
information the expert may have.
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