Re: [MLUG - DISCUSSION] statistical inference

[Stephen Montgomery-Smith <EMAIL:PROTECTED>]

Mike Miller wrote:
> On Mon, 5 Jun 2006, Jonathan King wrote:
>
> > On 6/5/06, Mike Miller <EMAIL:PROTECTED> wrote:
> >
> > > On Mon, 5 Jun 2006, Stephen Montgomery-Smith wrote:
> > > >
> > > > This problem is obviously important to ecology and is well studied: 
> > > > http://viceroy.eeb.uconn.edu/EstimateS.  Chao's work on this is 
> > > quite > brilliant, but is essentially ad-hoc.  I tried a Baysian 
> > > approach, > and its dependence upon priors is tremendous, and in any 
> > > case it > always seem to estimate too high.
> > >
> > > I think a Bayesian approach is very reasonable for a problem like 
> > > this one.  If it gives answers that appear incorrect, change the prior.
> >
> >
> > OK, so I think *this* is the difference between a mathematician like 
> > Stephen and people like Mike and I who can't go running away screaming 
> > from the data when there's a problem.  We shrug and say, "well, let's 
> > try something else".  For somebody like Stephen, a statement like 
> > "well, just try another prior" must seem horribly unprincipled.
>
>
>
> ;-)
>
> Well, science is messy and you have to do something!  There will never 
> be anything in science that is as tidy as anything in mathematics.  I 
> think the two tidiness distributions don't even overlap.

I don't think it is a matter of "principled."  It is a matter that I 
have come across a problem which clearly illustrates the problems with 
the current theory, but which is nevertheless easy to perform thought 
experiments with.  As such, it is the ideal kind of problem to try to 
explore the foundations of statistics.

Stephen

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