Solving Influence Diagrams Using Gibbs Sampling

  • Ali Jenzarli
Part of the Lecture Notes in Statistics book series (LNS, volume 112)


We describe a Monte Carlo method for solving influence diagrams. This method is a combination of stochastic dynamic programming and Gibbs sampling, an iterative Markov chain Monte Carlo method. Our method is especially useful when exact methods for solving influence diagrams fail.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bellman, R. and Dreyfus, S. (1962) Applied Dynamic Programming, Princeton University Press, Princeton, N.J.zbMATHGoogle Scholar
  2. Clemen, R.T. (1991) Making Hard Decisions, Duxbury Press, Belmont, California.Google Scholar
  3. Gelfand, A. E. and Smith, A. F. M. (1990) Sampling-based approaches to calculating marginal densities, Journal of the American Statistical Association, 85 (410), 398–409.MathSciNetzbMATHCrossRefGoogle Scholar
  4. Geman, S. and Geman, D. (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian estoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6, 721–741.CrossRefGoogle Scholar
  5. Hastings, W. K. (1970) Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57 (1), 97–109.zbMATHCrossRefGoogle Scholar
  6. Jensen, F. V., Lauritzen, S. L., and Olesen, K. G. (1990) Bayesian updating in causal probabilistic networks by local computations, Computational Statistics Quarterly 4, 269–282.MathSciNetGoogle Scholar
  7. Ndilikilikesha, P. (1992) Potential influence diagrams, Working Paper No. 235, School of Business, University of Kansas, Lawrence, Kansas.Google Scholar
  8. Olmsted, S. M. (1983) On representing and solving decision problems, Ph.D. thesis, Department of Engineering-Economic Systems, Stanford University, Stanford, CA.Google Scholar
  9. Shachter, R. D. (1986) Evaluating influence diagrams, Operations Research, 34 (6), 871–882.MathSciNetCrossRefGoogle Scholar
  10. Shenoy, P. P. (1992) Valuation-based systems for Bayesian decision analysis, Operations Research, 40 (3), 463–484.MathSciNetzbMATHCrossRefGoogle Scholar
  11. Shenoy, P. P. (1993) A new method for representing and solving Bayesian decision problems, in D. J. Hand (ed.), Artificial Intelligence Frontiers in Statistics: Al and Statistics III, 119–138, Chapman & Hall, London.Google Scholar
  12. Smith, J. E., Holtzman, S., and Matheson, J. E. (1993) Structuring conditional relationships in influence diagrams, Operations Research, 41 (2), 280–297.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Ali Jenzarli
    • 1
  1. 1.College of BusinessThe University of TampaTampaUSA

Personalised recommendations