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TEB: Explain average of ratios/ratio of averages better
- Subject: TEB: Explain average of ratios/ratio of averages better
- From: Chris Warburton
- Date: Tue, 29 May 2018 13:46:52 +0100
- Resolution: fixed
- State: resolved
Terminology may not be widely known, so we should explain the
difference. We should also include equations for each.
Note that "ratio of averages" seems weird if we do:
p = (n1 + n2 + ...) / (d1 + d2 + ...)
As Jianguo points out, we can instead write this as the average
numerator over the average denominator:
p = (n1 + n2 + ... / N) / (d1 + d2 + ... / N)
The 1/N factors cancel out, giving us the equation above, but putting
them in explicitly makes it clearer where the terminology comes from.
Also, get rid of 'Bernoulli process' stuff. It would require more
explanation, but actually is completely irrelevant to the rest of the
paper.
The average of the ratios is quite straightforward: it's the average,
and tells us the expected precision or recall. All *sets* are treated
equally, regardless of how large they are.
The ratio of the averages is slightly harder to explain: it's the pooled
average, it treats all *conjectures* equally, regardless of the set they
came from, and gives the expected wanted/not of a conjecture.
Maybe useful to talk about wanted/not as being true positives vs false
positives.