On 06 Mar 2014, at 16:40, Gabriel Bodeen wrote:
On Thursday, March 6, 2014 1:52:56 AM UTC-6, Bruno Marchal wrote:
On 05 Mar 2014, at 18:45, Gabriel Bodeen wrote:
Brent was right but the explanation could use some examples to show
you what's happening. The strangeness that you noticed occurs
because you're looking at cases where the proportion is *exactly*
50%.
binopdf(2,4,0.5)=0.375
binopdf(3,6,0.5)=0.3125
binopdf(4,8,0.5)=0.2374
binopdf(8,16,0.5)=0.1964
binopdf(1000,2000,0.5)=0.0178
binopdf(1e6,2e6,0.5)=0.0006
Instead let's look at cases which are in some range close to 50%.
binocdf(5,8,0.5)-binocdf(3,8,0.5)=0.4922
binocdf(10,16,0.5)-binocdf(6,16,0.5)=0.6677
binocdf(520,1000,0.5)-binocdf(480,1000,0.5)=0.7939
binocdf(1001000,2e6,0.5)-binocdf(999000,2e6,0.5)=0.8427
binocdf(1000050000,2e9,0.5)-binocdf(999950000,2e9,0.5)=0.9747
Basically, as you flip a coin more and more times, you get a
growing number of distinct proportions of heads and tails that can
come up, so any exact proportion becomes less likely. But at the
same time, as you flip the coin more and more times, the
distribution of proportions starts to cluster more and more tightly
around the expected value. So for tests when you do two million
flips of a fair coin, only about 0.06% of the tests come up exactly
50% heads and 50% tails, but 84.27% of the tests come up between
49.95% and 50.05%.
Good. So you agree with step 3? What about step 4? (*). I am
interested to know.
the FPI is just the elementary statistics of the "bernouilly
épreuve" (in french statistics), and that is pretty obvious when you
grasp the definitions given of 1p and 3p.
Bruno
(*) http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
Did you mean to address me, or did you mean to address Chris?
I don't object to any step in UDA. It seems internally consistent
and plausible to me. I'm unsure what level of confidence I would
assign to it being actually true, although my gut feeling is in the
vicinity of 25%.
A reasoning is 100% valid, or invalid. Do you mean that the truth of
the premise, comp, is in the vicinity of 25%. making perhaps its
neoplatonist consequences in the vicinity of 25% ?
I will make a confession: for me comp only oscillates between the
false and the unbelievable.
I have much formal logic to learn before I have any meaningful
opinion about AUDA.
OK. Fair enough to say. I often come back to zero, so you might enjoy
a ride eventually :)
Bruno
-Gabe
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