GENEALOGY-DNA-L Archives

Archiver > GENEALOGY-DNA > 2010-11 > 1291077726


From: James Heald <>
Subject: Re: [DNA] P value (was chances are, it's wrong)
Date: Tue, 30 Nov 2010 00:42:06 +0000
References: <F9C440A2-FC59-4A9E-AAAC-85DEE9D2FAB0@GMAIL.COM>, ,<COL115-W50D879F102DC3996D9D454A03A0@phx.gbl>, ,<4CE7A3C0.7050702@ucl.ac.uk>, ,<COL115-W1464B78AF0292D6AEFA183A03B0@phx.gbl>,<COL115-W5950BB2C58A31B4806036EA03B0@phx.gbl>,<4CE8088B.3020500@ucl.ac.uk>,<COL115-W45724B549DCDA5DD2EC4A0A03B0@phx.gbl> <COL115-W424C7732D1583F8960685CA03B0@phx.gbl> <4CE851AF.2030304@ucl.ac.uk> <REME20101122153113@alum.mit.edu><4CEC4709.9080606@ucl.ac.uk> <REME20101129170610@alum.mit.edu>
In-Reply-To: <REME20101129170610@alum.mit.edu>


> Also, it is silly (not to mention sneaky) to pretend that "95% CI" as
> used in the past ever meant an interval that was 95% credible.

On the other hand, it's a distinction that I have seen blurred often
enough...

But you're absolutely right. A "95% CI" is *not* an interval that is
95% credible, it is *not* an interval for which
P (theta within interval | data) = 95%
and if you work out what is the conditional probability
P (theta within interval | data)
then in general, some important special cases excepted, the answer will
not be 95%.

Now you're right: you don't have to be an out-and-out Frequentist to see
some value in keeping an eye on confidence intervals; but in general
the interval with a 95% conditional probability given the data typically
fits closer our desiderata for what we would like, rather than a CI that
achieves its *average* 95% coverage by being over-inclusive (covering an
interval with a conditional probability of more than 95%) for some data
values, to make up for other data values for which its interval has a
conditional probability much less than 95% given the data.

We're more likely to be interested in the probability of the interval
being 95% given the data we have had, rather than being 95% given the
unknown parameter, averaging over all the data we *might* have had but
in fact did *not* have.



On 29/11/2010 22:16, John Chandler wrote:
> James wrote:
>> It's important to keep clear that the distinction between (Frequentist)
>> confidence intervals on the one hand, and (Bayesian) credible intervals
>> on the other.
>
> That's just the point. The term "confidence interval" is NOT a
> Frequentist term, but rather a universal term, and it has always meant
> confidence in the estimate. You can't wipe away the literature at
> the stroke of a pen and say that people didn't mean what they meant
> when they wrote what they wrote. Also, it is silly (not to mention
> sneaky) to pretend that "95% CI" as used in the past ever meant an
> interval that was 95% credible.
>
>> (Indeed, a sufficiently fundamentalist Frequentist would deny the latter
>> concept is even meaningful, as they would object to the parameter -- a
>> thing considered to have a fixed, albeit unknown, actual value -- being
>> treated as a random variable).
>
> Nonetheless, a Frequentist must still acknowledge that the numerical
> result coming out of a calculation is an ESTIMATE of the parameter
> value, and a Bayesian must still acknowledge that we live in just one
> physical universe in which the underlying parameter does indeed have
> one fixed actual value (as long as the model itself is correct).
>
> John Chandler
>
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