Construction, Simulation and Testing of Causal Probabilistic Networks

  • U. G. Oppel
  • A. Hierle
  • M. Noormohammadian
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 363)


From the probabilistic point of view a complex system subject to vagueness, randomness and uncertainty may be characterized by a multivariate probability distribution. Such a multivariate distribution may he approximated by the sequence of empirical distributions of a properly chosen sample of realizations of the system, e.g. obtained from Monte Carlo simulations of the system or by properly collected data. But how to obtain these Monte Carlo simulations?

Another way of characterizing such a system is to use an ancestral causal probabilistic network (CPN). Such a CPN is a directed graph and a family of Markov kernels. The graph describes the dependencies of the subsystems qualitatively and the Markov kernels describe them quantitatively. The conditional probabilities of the Markov kernels may be interpreted as stochastic cause-effect relations. To such a CPN a directed Markov field is associated which is the joint multivariate distribution of the system.

The representation of multivariate distribution by a CPN has some advantages: it makes even complicated multivariate distributions storable and operable, it allows for Bayesian learning by introducing and propagating of evidence, it may serve for calculation of marginal distributions, and it may be used for Monte Carlo simulations of the system. These properties make it possible to evaluate the description of the system by the multivariate distribution and the CPN. This evaluation is based on comparison of marginal distributions of the multivariate distribution with empirical distributions obtained from Monte Carlo simulations and from data. The comparison may be based on properly chosen symmetric or asymmetric distances or statistical tests. We give some examples.


Monte Carlo Simulation Diabetic Nephropathy Expert System Joint Distribution Conditional Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Wien 1995

Authors and Affiliations

  • U. G. Oppel
    • 1
  • A. Hierle
    • 1
  • M. Noormohammadian
    • 1
  1. 1.University of MunichMunichGermany

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