Re: [MLUG - DISCUSSION] statistical inference

[Mike Miller <EMAIL:PROTECTED>]

On Mon, 5 Jun 2006, Jonathan King wrote:

> On 6/5/06, Stephen Montgomery-Smith <EMAIL:PROTECTED> wrote:
> > Mike Miller wrote:
> > >
> > > Sort of.  It really depends on the situation.  I'm not always sure 
> > > what drives arguments about "Bayesian" and "frequentist" perspectives 
> > > on inference, but I think a lot of it is due to the fact that it is a 
> > > difficult topic and a statistician can get by professionally without 
> > > ever really coming to grips with the core philosophical problems.
> >
> > My sense is that statistics as a field doesn't have the strong 
> > foundations that, say, math or physics has.  I think this field needs a 
> > "Newton" to come along and sort it all out.  But I also think that the 
> > time is ripe for this to happen, just like Einstein's theories were 
> > ripe for their time.
>
> I'm not sure the analogy is exact.  In one sense, statistics did already 
> have a Newton: Bayes Theorem is about as amazing and basic a thing as 
> you're ever likely to get in almost any field.  But what I think the 
> Reverend Bayes couldn't do (and arguably shouldn't have done) is tell us 
> what our priors should be.

Bayes actually introduced the uniform prior in his 1763 paper.  I had no 
idea until I read it.  It was pretty cool -- he developed an example where 
a ball is thrown into a square box and a line is then drawn in the box 
from left side to right side (perpendicular to the sides) and through the 
middle of the ball.  Then a second ball is thrown -- what is the 
probability that it ends up on the top side of the line?  That was his 
approach -- the tossing of the first ball provides the uniform prior for 
the second ball (or subsequent balls).

I'll just add that I agree with what Jon wrote, probably with all of it, 
and I think his example below about variation in capture probabilities is 
a very good example of an assumption that is hard to avoid and hard to 
justify.  Science is a messy business!  We just have to be clear on what 
we are doing and the limitations and biases inherent in any given model.


Stephen wrote:
> > The problem that has driven my thinking is this one.  Suppose you go 
> > out and capture 1000 birds.  You observe 16 different species, but 5 of 
> > them you only observe once.  Try to give a lower estimate on how many 
> > species you didn't observe.  Note that 0 is quite unlikely, because 5 
> > of the species are quite likely very sparse,

Jon replied:
> ....or are very good at eluding capture.  And I mention this not just to 
> be cute, but because this (the notion that species don't differ in their 
> capturability) is the kind of convenience assumption that you pretty 
> much have to make at first, but which is exactly what will mess with you 
> later.


Mike

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