Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Search-based methods to bound diagnostic probabilities in very large belief nets
Proceedings of the seventh conference (1991) on Uncertainty in artificial intelligence
Probabilistic reasoning in decision support systems: from computation to common sense
Probabilistic reasoning in decision support systems: from computation to common sense
Cost-based abduction and MAP explanation
Artificial Intelligence
Theoretical analysis and practical insights on importance sampling in Bayesian networks
International Journal of Approximate Reasoning
Review: learning bayesian networks: Approaches and issues
The Knowledge Engineering Review
Importance sampling algorithms for Bayesian networks: Principles and performance
Mathematical and Computer Modelling: An International Journal
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Several Artificial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncertain domain models. Even though the correct working of these schemes is practically contingent upon the existence of a small number of probable states, no formal justification has been proposed of why this should be the case. This paper attempts to fill this apparent gap by studying asymmetries among probabilities of various states of uncertain models. By rewriting the joint probability distribution over a model's variables into a product of individual variables' prior and conditional probability distributions and applying central limit theorem to this product, we can demonstrate that the probabilities of individual states of the model can be expected to be drawn from highly skewed lognormal distributions. With sufficient asymmetry in individual prior and conditional probability distributions, a small fraction of states can be expected to cover a large portion of the total probability space with the remaining states having practically negligible probability. Theoretical discussion is supplemented by simulation results and an illustrative real-world example.