Re: [MLUG - DISCUSSION] statistical inference

[Stephen Montgomery-Smith <EMAIL:PROTECTED>]

Mike Miller wrote:
> On Mon, 5 Jun 2006, Stephen Montgomery-Smith wrote:
>
> > I don't see Bayes Theorem as the answer.  I have tried some of these 
> > uninformative priors in my species counting problem, and they fail 
> > dramatically (they always predict that the number of species you 
> > haven't seen is zero).
>
>
> What model are you using?  It must be some sort of multinomial.

Yes, its a big multinomial.

>  I just 
> can't imagine how I would get zero as an answer.

The problem is that the uninformative prior distributions are not 
"proper," that is, they don't integrate up to 1 but to infinity.  So you 
get zeroes at the end if you haven't somehow mollified those infinities 
away.

Look at my answer to Jon for more details.

> Side note:  The problem reminds me of the problem of estimating both N 
> and p for a binomial random variable.  If you have a single observation, 
> you can estimate p given N or N given p, but you can't estimate both.  
> If you have one or more observations (say you observe counts of 5, 7 and 
> 9), and we assume N and p are fixed values, it is possible to estimate 
> both, but the confidence intervals will be huge, especially for N.  With 
> 5, 7, and 9 we have a mean of 7 so we would guess that Np = 7, but it is 
> hard to know if N = 1000 and p = .007 or, instead, N = 10 and p = .7.  I 
> remember a paper in JASA about 10-15 years ago on this topic.

That looks interesting.

> > Quite likely I am going to put a lot of thought into this problem next 
> > year (now I have other projects), but one possibility I am considering 
> > is that the Kolmogorov laws of probability don't always apply.
>
> Apply to what?  Kolmogorov's "laws"  are axioms and they create an 
> imaginary world in which they always apply.  In science we try to 
> construct an imaginary world (model) that mimics the real world.  It 
> would be convenient to construct a model where you can use Kolmogorov's 
> axioms, but I suppose it isn't necessary.

See my answer to Jon.

> > But I am considering an idealized "thought experiment" so I don't need 
> > to consider all of the practical problems.  And even this idealized 
> > thought experiment shows that Bayes Theorem just doesn't cut it.
>
> But how are you using it?

I gave a seminar to that Stats-Bayesian group the semester before last, 
and they agreed that I was following the standard Bayesian protocol.

Stephen

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