  We review and illustrate how the volatility smile translates into a
probability distribution, the market-implied probability distribution
representing believes priced in. The effects of changes in the smile are
examined. Special attention is given to the effects of slope, which might
appear at first counter-intuitive.
  We then show how Bayesian methods can be used to deal with sparse real market
data. With each skew in a parametric model we associate a probability. This is
illustrated with an example, for which multivariate parameter distributions are
derived. We introduce the fuzzy smile (or fuzzy skew) as a visual illustration
of the skew distribution.
