Allan Adler wrote:
>
> Thanks to Robert J. MacG. Dawson for explaining how binomial sampling
> is done.
>
> > If P is smaller, the interval width will be correspondingly smaller.
> >This breaks down if P is so small that NP < about 10; in the latter case
> >other methods can be used based on a Poisson distribution.
>
> Since we don't actually know what P is, how would we decide that it is
> more appropriate to use the Poisson distribution?
Using p to estimate it; or on the basis of previous knowledge about the
situation.
> > The big question is: are your independence assumptions valid? And that
> >depends on where the data come from. What works for a dictionary (which,
> >as I've explained, is not a scenario where your assumption that the
> >small book is better holds water) may not work for DNA sequencing or
> >tables of integrals or phone books.
>
> I look at it this way. If D1 (the smaller, allegedly more reliable, dictionary)
> didn't exist, people would use D2 (the more comprehensive, but allegedly
> less reliable, dictionary) and hope for the best while learning to navigate
> around its deficiencies. Since the need for the more comprehensive dictionary
> exists independently of the existence of D1, the decision a dictionary user
> has to make is whether to purchase and carry around both dictionaries or
> whether he/she can simply rely on D2. Therefore, it doesn't really matter
> whether the assumption is valid that the probability of a word being correct
> in D2 is independent of whether the word also occurs in D1. It only matters
> whether D2 is good enough at performing D1's job to make D1 unnecessary most
> of the time. That is why it is permissible to make the assumption, even if
> it isn't true.
Not at all. If a word is omitted from a dictionary you know it's not
there. If it's given with an inaccurate definition you are in trouble.
(Would you rather be stuck in a city where you do not speak the language
with a phrase book containing 200 accurate translations, or one with 200
accurate translations and another 1000 in the style of the Monty Python
Hungarian Phrasebook sketch:
======SLIGHTLY SILLY LINK WARNING==============
http://www.talpak.org/alakulat/python/jelenetek/hungarian.html
================================================
?)
This may not hold in other scenarios.
-Robert Dawson
.
.
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