On Feb 8, 2007, at 9:16 AM, gts wrote:
On Wed, 07 Feb 2007 16:51:18 -0500, Ben Goertzel <[EMAIL PROTECTED]>
wrote:
In fact I have been thinking about how one might attempt a dutch
book against Novamente involving your multiple component values,
but I do not yet fully understand b. My impression at the moment
is that b is similar to 'power' in conventional statistics -- a
real number from 0 to 1 that roughly speaking acts as a measure
of the robustness of the analysis. Fair comparison?
The power of a statistical hypothesis test measures the test's
ability to reject the null hypothesis when it is actually
false ... this has very little to do with indefinite or imprecise
probabilities...
Let me ask you in a different way:
Can b be regarded as a measure of Novamente's confidence in p?
Not exactly...
b represents the estimated chance that, after N more observations,
the estimated probaiblity of event S will lie in [L,U]
So, b is a measure of Novamente's confidence in the interval [L,U]
You can calculate a measure of Novamente's confidence in p from the
numbers <L,U,b,N> but I don't know an analytical formula for this. I
know how to do the calculation e.g. if one assumes a Bernoulli
process underlying the observations of S.
A very rough heuristic (this is NOT the correct formula assuming a
Bernoulli process) would go something like
W = U-L (width)
n = c W/(1-W)
(n is the total amount of evidence underlying the indefinite
probability; and c is a constant depending on b and N )
w = n/(n+k)
(w is the "weight of evidence" or "confidence" associated with the
probability estimate)
This heuristic behaves pretty much correctly but is not the formula
we get from assuming a Bernoulli process, the latter is more complex...
-- ben
All other things being equal, does b increase with N?
-gts
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