Approximating Joint Probability Distributions Given Partial Information

References

• Abbas AE. Entropy methods for joint distributions in decision analysis. IEEE Trans. Engrg. Management (2006) 53(1):146–159Crossref, Google Scholar
• Bélisle CJP, Romeijn HE, Smith RL. Hit-and-run algorithms for generating multivariate distributions. Math. Oper. Res. (1993) 18(2):255–266Link, Google Scholar
• Bertsekas DP. Nonlinear Programming (1999) 2nd ed.(Athena Scientific, Cambridge, MA) Google Scholar
• Bertsimas D, Tsitsiklis J. Introduction to Linear Optimization (1997) (Athena Scientific, Belmont, MA) Google Scholar
• Bickel JE, Smith JE. Optimal sequential exploration: A binary learning model. Decision Anal. (2006) 3(1):16–32Link, Google Scholar
• Boyd S, Vandenberghe L. Convex Optimization (2004) (Cambridge University Press, New York) Crossref, Google Scholar
• Clemen RT, Reilly T. Correlations and copulas for decision and risk analysis. Management Sci. (1999) 45(2):208–224Link, Google Scholar
• Delfiner P. Modeling dependencies between geologic risks in multiple targets. SPE Reservoir Eval. Engrg. (2003) 6:57–64SPA 82659-PACrossref, Google Scholar
• Devroye L. Non-Uniform Random Variate Generation (1986) (Springer-Verlag, New York) Crossref, Google Scholar
• Dyer JS, Farrell W, Bradley P. Utility functions for test performance. Management Sci. (1973) 20(4-Part I):507–519Link, Google Scholar
• Ireland CT, Kullback S. Contingency tables with given marginals. Biometrika (1968) 55(1):179–188Crossref, Google Scholar
• Jaynes ET. Information theory and statistical mechanics. Physical Rev. (1957) 106(4):620–630Part 1Crossref, Google Scholar
• Jaynes ET. Prior probabilities. IEEE Trans. Systems Sci. Cybernetics (1968) 4(3):227–241Crossref, Google Scholar
• Keefer DL. Underlying event model for approximating probabilistic dependence among binary events. IEEE Trans. Engrg. Management (2004) 51(2):173–182Crossref, Google Scholar
• Korsan RJ, Oliver RM, Smith JQ. Towards better assessments and sensitivity procedures. Influence Diagrams, Belief Nets and Decision Analysis (1990) (Wiley & Sons, New York) 427–454Google Scholar
• Kullback S, Leibler RA. On information sufficiency. Ann. Math. Statist. (1951) 22(1):79–86Crossref, Google Scholar
• Lovasz L. Hit-and-run mixes fast. Math. Programming (1998) 86(3):443–461Google Scholar
• Lowell DG. Sensitivity to relevance in decision analysis. (1994) . Ph.D. thesis, Engineering and Economic Systems, Stanford University, Stanford, CAGoogle Scholar
• MacKenzie GR. Approximately maximum entropy multivariate distributions with specified marginals and pairwise correlations. (1994) . Ph.D. thesis, University of Oregon, EugeneGoogle Scholar
• McMullen P. The maximum number of faces of a convex polytope. Mathematika (1970) 17(2):179–184Crossref, Google Scholar
• Montiel LV. Approximations, simulation, and accuracy of multivariate discrete probability distributions in decision analysis. (2012) . Ph.D. thesis, University of Texas at Austin, AustinGoogle Scholar
• Montiel LV, Bickel JE. Generating a random collection of discrete joint probability distributions subject to partial information. Methodology Comput. Appl. Probab. (2012a) . ePub ahead of print, May 22, http://link.springer.com/article/10.1007%2Fs11009-012-9292-9Google Scholar
• Montiel LV, Bickel JE. A simulation-based approach to decision making with partial information. Decision Anal. (2012b) 9(4):329–347Link, Google Scholar
• Moore LR, Mudford BS. Probabilistic play analysis from geoscience to economics: An example from the Gulf of Mexico. SPE 52955, SPE Hydrocarbon Econom. Evaluation Sympos. (1999) DallasCrossref, Google Scholar
• Moskowitz H, Sarin RK. Improving the consistency of conditional probability assessments for forecasting and decision making. Management Sci. (1983) 29(6):735–749Link, Google Scholar
• Sarin RK. A sequential approach to cross-impact analysis. Futures (1978) 10(1):53–62Crossref, Google Scholar
• Sarin RK. An approach for long term forecasting with an application to solar electric energy. Management Sci. (1979) 25(6):543–554Link, Google Scholar
• Schmidt BK, Mattheiss TH. The probability that a random polytope is bounded. Math. Oper. Res. (1977) 2(3):292–296Link, Google Scholar
• Sklar A. Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris (1959) 8:229–231Google Scholar
• Smith RL. Efficient Monte Carlo procedures for generating points uniformly distributed over bounded regions. Oper. Res. (1984) 32(6):1296–1308Link, Google Scholar
• Stabell CB. Alternative approaches to modeling risks in prospects with dependent layers. SPE 63204, SPE Annual Tech. Conf. Exhibition (2000) DallasCrossref, Google Scholar