**GENEALOGY-DNA-L Archives**

From:James Heald <>Subject:Re: [DNA] P value (was chances are, it's wrong)Date:Tue, 30 Nov 2010 00:42:06 +0000References:<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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**This thread:**

- [DNA] Odds Are, It's Wrong by Wilcox Lisa <>
- Re: [DNA] Odds Are, It's Wrong by Al Aburto <>
- Re: [DNA] Odds Are, It's Wrong by "Ken Nordtvedt" <>
- Re: [DNA] Odds Are, It's Wrong by Al Aburto <>

- Re: [DNA] Odds Are, It's Wrong by "Alister John Marsh" <>

- Re: [DNA] Odds Are, It's Wrong by "Ken Nordtvedt" <>

- Re: [DNA] Odds Are, It's Wrong - 5% of the time by Steven Bird <>
- Re: [DNA] Odds Are, It's Wrong - 5% of the time by Steven Bird <>

- Re: [DNA] Odds Are, It's Wrong - 5% of the time by Gareth Henson <>
- Re: [DNA] Odds Are, It's Wrong - 5% of the time by "Ken Nordtvedt" <>
- Re: [DNA] Odds Are, It's Wrong - 5% of the time by Wilcox Lisa <>
- Re: [DNA] Odds Are, It's Wrong - 5% of the time by "Ken Nordtvedt" <>

- Re: [DNA] Odds Are, It's Wrong - 5% of the time by Wilcox Lisa <>

- Re: [DNA] Odds Are, It's Wrong - 5% of the time by "Ken Nordtvedt" <>

- Re: [DNA] Odds Are, It's Wrong - 5% of the time by James Heald <>

- [DNA] Odds Are, It's Wrong - 5% of the time by "Lancaster-Boon" <>

- Re: [DNA] Odds Are, It's Wrong by Al Aburto <>