4 ms·

Definitely also check out interval arithmetic: https://en.wikipedia.org/wiki/Interval_arithmetic https://en.wikipedia.org/wiki/Interval_arithmetic Excellent ar

• enriquto 5y ago
  From my limited point of view, interval arithmetic looks particularly wrong for everything. It is as if we were using Bayes rule to update our knowledge of numbers after arithmetic operations (which is a good idea), but all the distributions were artificially changed to uniform after the update (which is obviously a very bad idea). Is there any practical application where interval arithmetic makes sense?
  • gugagore 5y ago
    The big problem with interval arithmetic, stated in terms of probability distributions, isn't that the distributions are uniform, but that the distributions are independent. The distribution of x-x is the degenerate distribution 0. But the naive implementation of uncertainty propagation would not take into account the dependence between x and x, and would give an over-approximation. It's true that probability distributions generalize sets, and sets generalize intervals. But there are many applications where intervals are a great choice for representing uncertainty. Changing a distribution to uniform is not obviously a bad idea because you can parameterize a uniform distribution and represent the parameters compactly. There is no compact representation for arbitrary distributions.
  • petters 5y ago
    It can find the global optimum for a function of a few variables.