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%. I have much formal logic to learn before I have any meaningful opinion about AUDA. -Gabe -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
