I assumed the question was “I have two endpoints of several intervals but that’s not enough to combine intervals”. My answer is “assume uniform over some natural scale”
My point is precisely that “[...] for combining estimates [...] assume a uniform distribution over some natural scale” doesn’t accomplish your stated goal of being able to combine estimates.
My point is precisely that “[...] for combining estimates [...] assume a uniform distribution over some natural scale” doesn’t accomplish your stated goal of being able to combine estimates.