I’m confused about what concrete question about candyfloss the example is trying to answer, But my usual heuristic for combining estimates is that in the absence of more information (or more realistically, more desire to investigate), I will assume a uniform distribution over some natural scale. For example 10k-40k is on magnitude, so pretend it’s uniform over log(10k) to log(40k). 50-8000 is also on magnitude.
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”. If the actual question is “I don’t know how to combine distributions, help” then I think my answer is “if you don’t already know the answer then probably you should simulate and if you can’t do that then I guess use Guesstimate because anything else will take too much scaffolding to reasonably learn”.
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.
I’m confused about what concrete question about candyfloss the example is trying to answer, But my usual heuristic for combining estimates is that in the absence of more information (or more realistically, more desire to investigate), I will assume a uniform distribution over some natural scale. For example 10k-40k is on magnitude, so pretend it’s uniform over log(10k) to log(40k). 50-8000 is also on magnitude.
Unfortunately, the product of two log-uniform distributions is not a log-uniform distribution...
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”. If the actual question is “I don’t know how to combine distributions, help” then I think my answer is “if you don’t already know the answer then probably you should simulate and if you can’t do that then I guess use Guesstimate because anything else will take too much scaffolding to reasonably learn”.
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.