Some Properties of Joint Probability Distributions
  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, log-normal 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.
