Distribution of Mutual Information

The mutual information of two random variables z and J with joint probabilities {7rij} is commonly used in learning Bayesian nets as well as in many other fields. The chances 7rij are usually estimated by the empirical sampling frequency nij In leading to a point estimate J(nijIn) for the mutual information. To answer questions like "is J (nij In) consistent with zero?" or "what is the probability that the true mutual information is much larger than the point estimate?"