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Operations Research, Systems Engineering and Industrial Engineering Commons™
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Articles 1 - 4 of 4
Full-Text Articles in Operations Research, Systems Engineering and Industrial Engineering
Generating A Random Collection Of Discrete Joint Probability Distributions Subject To Partial Information, Luis V. Montiel, J. Eric Bickel
Generating A Random Collection Of Discrete Joint Probability Distributions Subject To Partial Information, Luis V. Montiel, J. Eric Bickel
Eric Bickel
In this paper, we develop a practical and flexible methodology for generating a random collection of discrete joint probability distributions, subject to a specified information set, which can be expressed as a set of linear constraints (e.g., marginal assessments, moments, or pairwise correlations). Our approach begins with the construction of a polytope using this set of linear constraints. This polytope defines the set of all joint distributions that match the given information; we refer to this set as the “truth set.”We then implement aMonte Carlo procedure, the Hit-and- Run algorithm, to sample points uniformly from the truth set. Each sampled …
Discretization, Simulation, And Swanson’S (Inaccurate) Mean, J. Eric Bickel
Discretization, Simulation, And Swanson’S (Inaccurate) Mean, J. Eric Bickel
Eric Bickel
Swanson’s Mean (SM) is heavily used within the oil and gas industry to approximate continuous probability distributions such as the lognormal. In this paper, we document the errors induced by this practice, which, as we show, has no theoretical justification for any distribution other than the normal. In parallel, we review methods to discretize continuous distributions and compare these methods to Monte Carlo simulation. We demonstrate that the best discretization methods have an accuracy equivalent to that of tens of thousands of Monte Carlo trials.
Modeling Dependence Among Geologic Risks In Sequential Exploration Decisions, J. Eric Bickel, James E. Smith
Modeling Dependence Among Geologic Risks In Sequential Exploration Decisions, J. Eric Bickel, James E. Smith
Eric Bickel
Prospects in a common basin are likely to share geologic features. For example, if hydrocarbons are found at one location, they may be more likely to be found at other nearby locations. When making drilling decisions, we should be able to exploit this dependence and use drilling results from one location to make more informed decisions about other nearby prospects. Moreover, we should consider these informational synergies when evaluating multi-prospect exploration opportunities. In this paper, we describe an approach for modeling the dependence among prospects and determining an optimal drilling strategy that takes this information into account. We demonstrate this …
Optimal Sequential Exploration: A Binary Learning Model, J. Eric Bickel, James E. Smith
Optimal Sequential Exploration: A Binary Learning Model, J. Eric Bickel, James E. Smith
Eric Bickel
In this paper, we develop a practical and flexible framework for evaluating sequential exploration strategies in the case where the exploration prospects are dependent. Our interest in this problem was motivated by an oil exploration problem, and our approach begins with marginal assessments for each prospect (e.g., what is the probability that the well is wet?) and pairwise assessments of the dependence between prospects (e.g., what is the probability that both wells i and j are wet?). We then use information-theoretic methods to construct a full joint distribution for all outcomes from these marginal and pairwise assessments. This joint distribution …