How to Get Beyond Uniform When Applying MaxEnt to Interval Uncertainty

In many practical situations, the Maximum Entropy (MaxEnt) approach leads to reasonable distributions. However, in an important case when all we know is that the value of a random variable is somewhere within the interval, this approach leads to a uniform distribution on this interval – while our intuition says that we should have a distribution whose probability density tends to 0 when we approach the interval’s endpoints. In this paper, we show that in most cases of interval uncertainty, we have additional information, and if we account for this additional information when applying MaxEnt, we get distributions which are in perfect accordance with our intuition.