🚀 go-pugleaf

Georg W�tschner <georg.wuetschner@unibw-muenchen.de> wrote:

[...]
> Maybe something which could point in the same direction was the so
> called weather problem a friend told me of:
> If one weather station states that tomorrow it will rain with a
> probability of 60%, and a second, which operates which totally different
> methods (->independent), predicts rain wiht 70% prob., then one can
> somehow calulate that it will rain with a prob. of, say, 80% (higher
> than the higher of the two)... any idea how this works?

If I'm not mistaken, the combined probability (whatever scheme you
find for doing the combining) will be a convex linear combination
of the individual probabilities, i.e., a linear combination of the
form sum_i a_i p_i, with all a_i >= 0 and sum_i a_i = 1.
This implies that the combined probability must be somewhere between
the least and greatest individual probabilities.

I think the topic you want to look into is called "combining experts"
or "combining opinions". Here is a reference:

 Genest, C. and Zidek, J. V. (1986), "Combining Probability Distributions: 
 A Critique and an Annotated Bibliography," Statistical Science 1 114--135.

For what it's worth,
Robert Dodier
--
``Prediction is extremely difficult. Especially about the future.''
 -- Niels Bohr