**GENEALOGY-DNA-L Archives**

From:James Heald <>Subject:Re: [DNA] FW: Odds Are, It's Wrong - 5% of the timeDate:Sun, 21 Nov 2010 00:14:21 +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><AANLkTi=mPBovTQGxXnLcYN+jG5-JNBK2ZNzqR3AHUHoo@mail.gmail.com>In-Reply-To:<AANLkTi=mPBovTQGxXnLcYN+jG5-JNBK2ZNzqR3AHUHoo@mail.gmail.com>On 20/11/2010 21:24, Robert Stafford wrote:

> I am not sure how this applies to TMRCA calculations. What is the null

> hypothesis you are testing? What do the Bayesians use as the confidence

> interval for TMRCA?

>

> Bob Stafford

Hi Bob,

I've talked a bit more about this in the post I've just made in the new

"P value" thread.

Basically, if the Frequentist upper confidence limit is 50 generations,

the null hypothesis is that the true number of generations is more than

50. For each of those values, in fewer than 5% of cases such a number

of generations would give n mutations or fewer; so the promise made is

that *if* the number of generations falls outside the confidence range,

*then* the confidence range would be wrongly accepted less than 5% of

the time.

However the counterpoint to this, as I pointed out in the other thread,

is that there are a lot more numbers more than 50 than there are less

than 50, so *given* that n mutations have been observed, it may actually

be more likely to be a rare event from a (comparatively common) large

number of generations, than a common event from a (comparatively rare)

small number of generations.

Hence the Bayesian alternative approach, which is to actually (try to)

work out the probability distribution for the number of generations

given the number of mutations, using eg Bruce Walsh's TMRCA calculator

http://nitro.biosci.arizona.edu/ftdna/TMRCA.html

for pairs of haplotypes, or software like BATWING to estimate the

probability distribution for the coalescence time given multiple haplotypes.

Then, having estimated the probability distribution, rather a confidence

interval, Bayesians will instead quote a "credibility interval" -- an

interval that contains 95% of the probability distribution just calculated.

Unlike confidence intervals therefore, the Bayesians quote an interval

in which, as a result of their calculations and modelling, they estimate

there to be a 95% chance of containing the true value.

In the above, I've deliberately glossed over the idea of one-sided and

two-sided intervals, so whether we should really be talking about 5% or

2.5% being the probability at issue in the tails; but if we were to

pin one end of the Bayesian interval at zero, then the Bayesian

credibility interval would be from there up until the point where 95% of

the probability has been accounted for, with only 5% chance of being

beyond that point.

Arguably, this is usually the notion people are actually looking for,

when they ask for the range of possibilites.

**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 <>