In recent posts, I've looked at the interpretation of the Shannon entropy, and the justification for the maximum entropy principle in inference under uncertainty. In the latter case, we looked at how mathematical investigation of the entropy function can help with establishing prior probability distributions from first principles.

There are some prior distributions, however, that we know automatically, without having to give the slightest thought to entropy. If the maximum entropy principle is really going to work, the first thing it has got to be able to do is to reproduce those distributions that we can deduce already, using other methods.