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Archiver > GENEALOGY-DNA > 2011-06 > 1307668069


From: David Johnston <>
Subject: Re: [DNA] Asymptotic Distributions for General Mutation Models
Date: Thu, 09 Jun 2011 20:07:49 -0500
References: <972D673E3D084E2DBBD515DD90077C82@kenPC> <000001cc2606$b16669c0$14333d40$@com> <4DEFBCFF.6040501@gmail.com> <000001cc2610$d0ce1240$726a36c0$@com> <4DEFD211.60207@gmail.com><000001cc26db$a4d9eb20$ee8dc160$@com>
In-Reply-To: <000001cc26db$a4d9eb20$ee8dc160$@com>


I am not sure what you mean by diabolically poor. Do you know of
anything better?

My point is that if IAM is close enough to the exact Likelihood
(exponential times modified Bessel function) than it is pretty much
optimal. Once you have calculated the true Likelihood for T=TMRCA, you
are pretty much done. You can't do better. There is some mathematical
theory called the Cramer Rao bound that gives a lower limit to the
variance (i.e. uncertainty) of any unbiased estimator of a parameter.

To simplify a bit: once you have calculated the true likelihood of T and
estimated T as the maximum likelihood value, you can't do any better.
There just isn't any more information in the data.

So IAM model can only be poor when it gives an answer different from the
exact likelihood calculation. That happens only when multiple mutations
per allele start to become fairly likely. But for close relatives on the
1000 year time-scale or less, it does about as well as you can do.

I know you have ideas about using off-modal matches but that is a little
different. That is using more information not just the data for the two
people. So that could improve things somewhat. But that shouldn't be
used as a criticism of IAM. It would be a criticism of sticking with
purely pairwise data to estimate their TMRCA via the method of Likelihoods.
Dave

On 6/9/11 2:30 PM, Sandy Paterson wrote:
>> Infinite Alleles gets too much criticism. It is a perfectly valid
>> approximation for many cases. It works well for close relations.
>>
> Am I misunderstanding what you mean by close relations? I took it to mean
> closely related. The IA model seems diabolically poor in estimating TMRCA
> for closely related people.
>
> I'll try to understand
>
> P(tau)=exp(-tau (1-k)) * (1-exp(-tau)^(k)).
>
> compared to
>
> P(T) = exp(-tau)*I_k(tau).
>
> tomorrow, but I don't hold out much hope.
>
>
> -----Original Message-----
> From:
> [mailto:] On Behalf Of David Johnston
> Sent: 08 June 2011 20:49
> To:
> Subject: Re: [DNA] Asymptotic Distributions for General Mutation Models
>
> I am not sure what that has to do with it. The question is whether the
> infinite alleles approximation
>
>
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