The MEP doesn't work if you assume you know statistics that you don't. Using a thousand statistics from a data sample should not be done because what you measure from the data sample aren't exactly the statistics from the true distribution.
Right, but what people use the MEP for in practice is to do statistical modeling: one has a data set of outcomes and attempts to build a statistical model of it. So you never know any statistic - even the mean - with absolute confidence.
After having read the related chapters of Jaynes' book I was fairly amazed by the Principle of Maximum Entropy, a powerful method for choosing prior distributions. However it immediately raised a large number of questions.
I have recently read two quite intriguing (and very well-written) papers by Jos Uffink on this matter:
Can the maximum entropy principle be explained as a consistency requirement?
The constraint rule of the maximum entropy principle
I was wondering what you think about the principle of maximum entropy and its justifications.