[R-sig-eco] (no subject)

[Nicholas Lewin-Koh]

Hi,
Mark Taper, Subhash Lele, and I organized an ESA invited session around
this topic 
at the 98? ESA meeting in Baltimore MD. Which resulted in 
Mark L. Taper and Subhash R. Lele (eds): The Nature of Scientific
Evidence: Statistical, Philosophical, and Empirical Considerations 
University of Chicago Press. 

Ok shameless self promotion aside, I think there is a little more
to the argument that Edwards and Royall are putting forward, and how it
differs from the frequentist
approach. Once the likelihood (model) is specified, the sampling/design
is ancillary (Basu's Theorem),
than the comparison of two competing models is the likelihood ratio. The
p-value than adds the additional 
layer of a not very informative null model. The idea here is that the
sampling or design should dictate the model
and then competing models should be assessed by the strength of evidence
given the data. I think far more interesting
is how well does this translate to non-nested models, ie competing
mechanisms. 

I don't think that Royall and Edwards are alone, however the Bayesian
approach
is usually what is suggested as the alternative, and has its own can of
worms. 
There are some other interesting approaches as well, such as the notion
of model adequacy. 
I think in Ecology we are rarely interested in the false comfort a
p-value provides,
we are more often interested in the evidence for competing mechanisms,
or prediction
of future outcomes.

My 2c

Nicholas

> Date: Sun, 28 Sep 2008 21:55:22 -0300
> From: " Paulo In?cio de Knegt L?pez de Prado "	<prado at ib.usp.br>
> Subject: [R-sig-eco] Are likelihood approaches frequentist?
> To: r-sig-ecology at r-project.org
> Message-ID: <20080929002804.M94451 at ib.usp.br>
> Content-Type: text/plain;	charset=iso-8859-1
> 
> Dear r-sig-ecology users
> 
> Here follow the messages I exchanged with Ben Bolker last week about the
> likelihood and frequentist approaches. We both would like to open this
> topic
> for discussion in the list.
> 
> Best wishes
> 
> Paulo
> 
> ----------------------------------------------------------------------------
> Dear Dr. Bolker, 
> 
> I am puzzled why some authors treat likelihood approaches as 
> frequentist, as it seems you did in page 13 of your book 'Ecological
> Models
> and Data'. 
> This sounds odd to me because  what brought my attention to likelihood
> was
> Richard Royall's book 'Statistical Evidence'. His framing of a paradigm
> based on the likelihood principle, and the clear distinction he makes
> between this paradigm and frequentist and Bayesian approaches looks
> quite convincing to me.
> 
> I agree with him that we use likelihood criteria to identify, among
> competing hypotheses, which one attribute the highest probability to  a
> given dataset. If I understood correctly, this is what Royal calls the
> 'evidence value' of a data set to a hypothesis 'vis a vis' other
> hypotheses. I also like his idea that the role of statistics in science
> is just to gauge this evidence value, no less, no more.
> 
> This approach differs from the frequentist because the sampling
> space is irrelevant, that is, other datasets that might be observed do
> not
> affect the evidence value of the observed data set. My favourite example
> is
> the comparison of binomial and negative binomial experiments on coin
> tossing, in the sections 1.11 and 1.12 of his book.
> 
> I am not an "orthodox likelihoodist"; on the contrary, I agree with the
> pragmatic view you express in your book. I'd just like to understand
> the key differences among the available statistical tools, in order to
> make
> a good pragmatic use of them. I'd really appreciate if you can help me
> with this.
> 
> Best wishes
> 
> Paulo
> -----------------------------------------------------------------------------
> >   Very well put.  Royall, and Edwards (author of _Likelihood_, Johns
> > Hopkins 1992) are what I would call "pure", or "hard-core",
> > or "orthodox", likelihoodists. They are satisfied with a statement
> > of relative likelihood, and don't feel the need to attach a p-value
> > to the result in order to have a decision rule for hypothesis rejection.
> >
> >   Far more commonly, however, people impose (? add ?) an additional
> > layer of frequentist procedure on top of this basic structure, namely
> > using the likelihood ratio test to assess the statistical significance
> > of a given observed likelihood ratio and/or to set a cutoff value
> > for profile confidence intervals.  Using the LRT puts the inference
> > back squarely into the frequentist domain, although the sample space
> > we are now dealing with (sample space of likelihoods derived from
> > coin-tossing experiments) is quite different from the one
> > we started with (sample space of outcomes of coin-tossing experiments).
> > As far as I can see, Edwards and Royall are almost alone in their
> > adherence to "pure" likelihood -- most of the rest of us pander
> > to the desire for p-values (or, less cynically, to the desire
> > for a probabilistically sound decision rule).
> >
> >  I would also add that different scientists have different
> > goals (belief, prediction, decision, assessing evidence). I too
> > think Royall makes a good case for the primacy of
> > assessing strength-of-evidence, and he gives the clearest
> > explanation I have seen, but I wouldn't completely
> > rule out the other frameworks.
> >
> >   Hope that makes sense -- thanks for the kind words!
> >
> >   cheers
> >    Ben Bolker 
> 
> --
> Paulo In?cio de Knegt L?pez de Prado
> Depto. de Ecologia - Instituto de Bioci?ncias - USP
> 
> 
> 
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> End of R-sig-ecology Digest, Vol 6, Issue 15
> ********************************************