A Framework for Solving Hybrid Influence Diagrams Containing Deterministic Conditional Distributions
Published Online:1 Mar 2012https://doi.org/10.1287/deca.1120.0230
References
- . Decision analysis by augmented probability simulation. Management Sci. (1999) 45(7):995–1007Link, Google Scholar
- . The pricing of options and corporate liabilities. J. Political Econom. (1973) 81(3):1323–1352Crossref, Google Scholar
- . Numerical Analysis (2010) 9th ed.(Brooks Cole, Boston) Google Scholar
- . A forward-backward Monte Carlo method for solving influence diagrams. Internat. J. Approximate Reasoning (2006) 42(1–2):119–135Crossref, Google Scholar
- . Multi-stage Monte Carlo method for solving influence diagrams using local computation. Management Sci. (2004) 50(3):405–418Link, Google Scholar
- . Arc reversals in hybrid Bayesian networks with deterministic variables. Internat. J. Approximate Reasoning (2009) 50(5):763–777Crossref, Google Scholar
- . Influence diagrams with continuous decision variables and non-Gaussian uncertainties. Decision Anal. (2007) 4(3):136–155Link, Google Scholar
- , Bacchus F, Jaakkola T. Hybrid Bayesian networks with linear deterministic variables. Uncertainty in Artificial Intelligence: Proc. 21st Conf. (2005a) (AUAI Press, Corvallis, OR) 136–144Google Scholar
- , Godo L. Nonlinear deterministic relationships in Bayesian networks. Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 8th European Conf., ECSQARU 2005 (2005b) (Springer, Berlin) 27–38Lecture Notes in Artificial Intelligence 3571Crossref, Google Scholar
- . Decision making with hybrid influence diagrams using mixtures of truncated exponentials. Eur. J. Oper. Res. (2008) 186(1):261–275Crossref, Google Scholar
- . Approximating probability density functions in hybrid Bayesian networks with mixtures of truncated exponentials. Statist. Comput. (2006) 16(3):293–308Crossref, Google Scholar
- . The physical interpretation of the quantum dynamics. Proc. Royal Soc. London, Ser. A (1927) 113(765):621–641Crossref, Google Scholar
- . The Principles of Quantum Mechanics (1958) 4th ed.(Oxford University Press, London) Crossref, Google Scholar
- . The Americal put option valued analytically. J. Finance (1984) 39(5):1511–1524Crossref, Google Scholar
- . Risk analysis in capital investment. Harvard Bus. Rev. (1964) 42(1):95–106Google Scholar
- . Generalised Functions (1979) (Ellis Horwood, Chichester, UK) Google Scholar
- . Proximal decision analysis. Management Sci. (1971) 17(9):845–879Link, Google Scholar
- , Howard RA, Matheson JE. Influence diagrams. Readings on the Principles and Applications of Decision Analysis (1984) II(Strategic Decisions Group, Menlo Park, CA) 719–762Google Scholar
- . Influence diagrams. Decision Anal. (2005) 2(3):127–143Link, Google Scholar
- . Generalized Functions: Theory and Technique (1998) 2nd ed.(Birkhaüser, Boston) Google Scholar
- . Three-point approximations for continuous random variables. Management Sci. (1983) 29(5):595–609Link, Google Scholar
- . Quantile-parameterized distributions. Decision Anal. (2011) 8(3):206–219Link, Google Scholar
- , Geiger D, Shenoy PP. Nonuniform dynamic discretization in hybrid networks. Uncertainty in Artificial Intelligence: Proc. 13th Conf. (1997) (Morgan Kaufmann, San Francisco) 302–313Google Scholar
- . Factor graphs and the sum-product algorithm. IEEE Trans. Inform. Theory (2001) 47(2):498–519Crossref, Google Scholar
- . On information and sufficiency. Ann. Math. Statist. (1951) 22:76–86Crossref, Google Scholar
- . Representing and solving decision problems with limited information. Management Sci. (2001) 47(9):1235–1251Link, Google Scholar
- , Grünwald P, Spirtes P. Solving hybrid influence diagrams with deterministic variables. Uncertainty in Artificial Intelligence: Proc. 26th Conf. (2010) (AUAI Press, Corvallis, OR) 322–331Google Scholar
- . Discrete approximations of probability distributions. Management Sci. (1983) 29(3):352–362Link, Google Scholar
- , Benferhat S, Besnard P. Mixtures of truncated exponentials in hybrid Bayesian networks. Symbolic and Quant. Approaches to Reasoning with Uncertainty: 6th Eur. Conf., ECSQARU-2001 (2001) (Springer, Berlin) 156–167Lecture Notes in Artificial Intelligence 2143Crossref, Google Scholar
- . On representing and solving decision problems. (1983) . Ph.D. thesis, Department of Engineering-Economic Systems, Stanford University, Stanford, CAGoogle Scholar
- , Kautz H, Porter B. Sampling methods for action selection in influence diagrams. Proc. 17th National Conf. Artificial Intelligence (2000) (AAAI Press, Menlo Park, CA) 378–385Google Scholar
- . Decision analysis with continuous and discrete variables: A mixture distribution approach. (1994) . Ph.D. thesis, Department of Engineering-Economic Systems, Stanford University, Stanford, CAGoogle Scholar
- , Heckerman D, Mamdani A. Mixtures of Gaussians and minimum relative entropy techniques for modeling continuous uncertainties. Uncertainty in Artificial Intelligence: Proc. 9th Conf. (1993) (Morgan Kaufmann, San Francisco) 183–190Crossref, Google Scholar
- . Gaussian influence diagrams. Management Sci. (1989) 35(5):527–550Link, Google Scholar
- . Valuation-based systems for Bayesian decision analysis. Oper. Res. (1992) 40(3):463–484Link, Google Scholar
- . Two issues in using mixtures of polynomials for inference in hybrid Bayesian networks. Internat. J. Approximate Reasoning (2012) . ePub ahead of print February 7, http://dx.doi.org/10.1016/j.ijar.2012.01.008Crossref, Google Scholar
- , Shachter RD, Levitt T, Lemmer JF, Kanal LN. Axioms for probability and belief-function propagation. Uncertainty in Artificial Intelligence 4 (1990) (North-Holland, Amsterdam) 169–198Crossref, Google Scholar
- . Extended Shenoy-Shafer architecture for inference in hybrid Bayesian networks with deterministic conditionals. Internat. J. Approximate Reasoning (2011a) 52(6):805–818Crossref, Google Scholar
- . Inference in hybrid Bayesian networks using mixtures of polynomials. Internat. J. Approximate Reasoning (2011b) 52(5):641–657Crossref, Google Scholar
- . Some practical issues in inference in hybrid Bayesian networks with deterministic conditionals. IEEE Proc. 2011 Eleventh Internat. Conf. Intelligent Systems Design Appl. (ISDA-11) (2011) (IEEE Research Publishing Services, Piscataway, NJ) 605–610Crossref, Google Scholar
- . Moment methods for decision analysis. Management Sci. (1993) 39(3):340–358Link, Google Scholar
- . Dynamic programming and influence diagrams. IEEE Trans. Systems, Man and Cybernetics (1990) 20(2):365–379Crossref, Google Scholar
- . Lagrange interpolation on Chebyshev points of two variables. J. Approximation Theory (1996) 87(2):220–238Crossref, Google Scholar

