Re: [MLUG - DISCUSSION] statistical inference

[Mike Miller <EMAIL:PROTECTED>]

On Tue, 6 Jun 2006, Jonathan King wrote:

> On 6/6/06, Mike Miller <EMAIL:PROTECTED> wrote:
> > Maybe part of the problem is that you have to distinguish between the 
> > multinomial and the multivariate hypergeometric.  Your distribution 
> > really should be multivariate hypergeometric and not multinomial.  The 
> > difference is that the multivariate hypergeometric is sampling without 
> > replacement while the multinomial is sampling with replacement.
>
> Actually, I thought he was sampling with replacement?  Or was that the 
> related problem.

I don't know.  I was just assuming that people would go out and capture a 
bunch of animals and count them, but maybe they capture one, release it, 
and continue to capture more animals.  Then it would be a straight 
multinomial problem.


> I think one of the really big issues here is that this isn't just a 
> cheesy 2 or 3 category multinomial.

Definitely.  It's an unknown number of categories.  It might be 
informative to study 2 and three category problems though.  What happens 
if you have either 2 or 3 species of animals, you aren't sure which, and 
you go out and capture 100 animals and they are only of two species. 
What is the probability that the third species exists but it wasn't 
captured?

Can this be extended by an inductive method where we repeatedly ask "if we 
know that n species exist, what is the probability than an n+1st species 
exists that was not observed?


> > I don't know how much of a difference that will make, but it is at 
> > least better conceptually.
>
> I guess you could take the w/replacement problem and recast it as a w/o 
> replacement problem if you've marked the units you are drawing from the 
> urn (so to speak) and then just ignore them if they come out again, 
> right?

Definitely.


> Meanwhile, since we've purged this thread of most of the list, I guess 
> this is my chance to ask: do either of you have recommendations for 
> recent, readable stuff on circulant or nearly circulant matrices?

Sorry.  I first heard of a circulant matrix when I read your question!
I'm sure you are aware of this free text:

http://www-ee.stanford.edu/~gray/toeplitz.pdf

It is mostly old but has been revised as recently as this year:

http://www-ee.stanford.edu/~gray/toeplitz.html

Mike

_______________________________________________
discussion mailing list
EMAIL:PROTECTED
http://mlug.missouri.edu/mailman/listinfo/discussion