Influence Diagrams with Continuous Decision Variables and Non-Gaussian Uncertainties

References

• Bazaraa M. S., Sherali H. D., Shetty C. M.Nonlinear Programming: Theory and Algorithms (1993) (Wiley, New York) Google Scholar
• Bielza C., Müller P., Rios Insua D. Decision analysis by augmented probability simulation. Management Sci. (1999) 45(7):995–1007Link, Google Scholar
• Boutilier C. The influence of influence diagrams on artificial intelligence. Decision Anal. (2005) 2(4):229–231Link, Google Scholar
• Buede D. M. Influence diagrams: A practitioner's perspective. Decision Anal. (2005) 2(4):235–237Link, Google Scholar
• Charnes J. M., Shenoy P. P. Multi-stage Monte Carlo method for solving influence diagrams using local computation. Management Sci. (2004) 50(3):405–418Link, Google Scholar
• Cobb B. R., Studený M., Vomlel J. Continuous decision MTE influence diagrams. Proc. Third Eur. Workshop Probabilistic Graphical Models (PGM–06) (2006) (Action M Agency, Prague) 67–74Google Scholar
• Cobb B. R., Shenoy P. P., Bacchus F., Jaakkola T. Hybrid Bayesian networks with linear deterministic variables. Uncertainty in Artificial Intelligence: Proc. Twenty-First Conf. (2005) (AUIA Press, Corvallis, OR) 136–144Google Scholar
• Cobb B. R., Shenoy P. P. Inference in hybrid Bayesian networks using mixtures of truncated exponentials. Internat. J. Approx. Reason. (2006) 41(3):257–286Crossref, Google Scholar
• Cobb B. R., Shenoy P. P. Decision making with hybrid influence diagrams using mixtures of truncated exponentials. Eur. J. Oper. Res. (2007) . ForthcomingGoogle Scholar
• Cobb B. R., Shenoy P. P., Rumí R. Approximating probability density functions in hybrid Bayesian networks with mixtures of truncated exponentials. Statist. Comput. (2006) 16(3):293–308Crossref, Google Scholar
• Detwarasiti A., Shachter R. D. Influence diagrams for team decision analysis. Decision Anal. (2005) 2(4):207–228Link, Google Scholar
• Göx R. F. Capacity planning and pricing under uncertainty. J. Management Accounting Res. (2002) 14(1):59–78Crossref, Google Scholar
• Howard R. A., Matheson J. E., Howard R. A., Matheson J. E. Influence diagrams. Readings on the Principles and Applications of Decision Analysis II (1984) (Strategic Decisions Group, Menlo Park, CA) 719–762[Reprinted in 2005, Decision Anal. 2(3) 127–143]Google Scholar
• Howard R. A., Matheson J. E. Influence diagram retrospective. Decision Anal. (2005) 2(3):144–147Link, Google Scholar
• Lauritzen S. L., Nilsson D. Representing and solving decision problems with limited information. Management Sci. (2001) 47(9):1238–1251Link, Google Scholar
• Lerner U., Segal E., Koller D., Breese J., Koller D. Exact inference in networks with discrete children of continuous parents. Uncertainty in Artificial Intelligence: Proc. Seventeenth Conf. (2001) (Morgan Kaufmann, San Francisco, CA) 319–328Google Scholar
• Madsen A. L., Jensen F. Solving linear-quadratic conditional Gaussian influence diagrams. Internat. J. Approx. Reason (2005) 38(3):263–282Crossref, Google Scholar
• Moral S., Rumí R., Salmerón A., Besnard P., Benferhart S. Mixtures of truncated exponentials in hybrid Bayesian networks. Symbolic and Quantitative Approaches to Reasoning under Uncertainty: Lecture Notes in Artificial Intelligence (2001) 2143(Springer-Verlag, Heidelberg, Germany) 156–167Crossref, Google Scholar
• Moral S., Rumí R., Salmerón A., Gamez J. A., Salmerón A. Estimating mixtures of truncated exponentials from data. Proc. First Eur. Workshop on Probabilistic Graphical Models (PGM–02) (2002) Cuenca, Spain:135–143Google Scholar
• Moral S., Rumí R., Salmerón A., Nielsen T. D., Zhang N. L. Approximating conditional MTE distributions by means of mixed trees. Symbolic and Quantitative Approaches to Reasoning under Uncertainty: Lecture Notes in Artificial Intelligence (2003) 2711(Springer-Verlag, Heidelberg, Germany) 173–183Crossref, Google Scholar
• Murphy K., Laskey K. B., Prade H. A variational approximation for Bayesian networks with discrete and continuous latent variables. Uncertainty in Artificial Intelligence: Proc. Fifteenth Conf. (1999) (Morgan Kaufmann, San Francisco, CA) 457–466Google Scholar
• Olmsted S. M. On representing and solving decision problems. (1983) . Doctoral thesis, Department of Engineering—Economic Systems, Stanford University, Stanford, CAGoogle Scholar
• Pauker S. G., Wong J. B. The influence of influence diagrams in medicine. Decision Anal. (2005) 2(4):238–244Link, Google Scholar
• Pearl J. Influence diagrams: Historical and personal perspectives. Decision Anal. (2005) 2(4):232–234Link, Google Scholar
• Poland W. B. Decision analysis with continuous and discrete variables: A mixture distribution approach. (1994) . Doctoral thesis, Department of Engineering—Economic Systems, Stanford University, Stanford, CAGoogle Scholar
• Poland W. B., Shachter R. D., Heckerman D., Mamdani E. H. Mixtures of Gaussians and minimum relative entropy techniques for modeling continuous uncertainties. Uncertainty in Artificial Intelligence: Proc. Ninth Conf. (1993) (Morgan Kaufmann, San Francisco, CA) 183–190Crossref, Google Scholar
• Rumí R., Salmerón A. Approximate probability propagation with mixtures of truncated exponentials. Internat. J. Approx. Reason. (2007) 45(2):191–210Crossref, Google Scholar
• Shachter R. D. Evaluating influence diagrams. Oper. Res. (1986) 34(6):871–882Link, Google Scholar
• Shachter R. D., Kenley C. R. Gaussian influence diagrams. Management Sci. (1989) 35(5):527–550Link, Google Scholar
• Shenoy P. P., Hand D. J. A new method for representing and solving Bayesian decision problems. Artificial Intelligence Frontiers in Statistics: AI and Statistics III (1993) (Chapman and Hall, London, UK) 119–138Crossref, Google Scholar
• Tatman J. A., Shachter R. D. Dynamic programming and influence diagrams. IEEE Trans. Syst. Man Cybernetics (1990) 20(2):365–379Crossref, Google Scholar
• Winkler R. L.An Introduction to Bayesian Inference and Decision (1972) (Holt, Rinehart, and Winston, New York) Google Scholar
• Winkler R. L., Hays W. L.Statistics: Probability, Inference, and Decisions (1970) (Holt, Rinehart, and Winston, New York) Google Scholar