This is “the subject of any of several theories involving models of uncertainty that do not assume a unique underlying probability distribution, but instead correspond to a set of probability distributions….Theories of imprecise probabilities are often expressed in terms of a lower probability measure giving the lower probability for every possible event from some universal set, or in terms of closed convex sets of probability distributions. Interval probabilities, Dempster-Shafer structures and probability boxes can be regarded as special-cases of imprecise probabilities” (Ferson et al., 2004, pp. 124-125).
Published in Chapter:
Probabilistic Methods for Uncertainty Quantification
N. Chugunov (Institute for Systems Analysis – Russian Academy of Sciences, Russia), G. Shepelyov (Institute for Systems Analysis – Russian Academy of Sciences, Russia), and M. Sternin (Institute for Systems Analysis – Russian Academy of Sciences, Russia)
Copyright: © 2008
|Pages: 11
DOI: 10.4018/978-1-59904-843-7.ch082
Abstract
The complexity and interdisciplinary nature of modern problems are often coupled with uncertainty inherent to real-life situations. There is a wide class of real-world problems described by well-formulated quantitative models for which a decision maker (DM) has to deal with uncertainty in values of initial parameters for these models. A good example of such a problem is hydrocarbon reservoir assessment in the exploration stage, which requires the involvement and joint consideration of geological, petroleum engineering, and financial models of reservoir exploration. The consequences of some unreasonable decisions can lead to millions of dollars in loss to the companies as it happens in the oil business, where industry sources on investment decision analysis continue to report surprise values (outside the [P10;P90] range) far more than the 20% indicated by this interval (Welsh, Begg, Bratvold, & Lee, 2004).