GENEALOGY-DNA-L Archives

Archiver > GENEALOGY-DNA > 2011-06 > 1307739200


From: "Kenneth Nordtvedt" <>
Subject: Re: [DNA] Asymptotic Distributions for General Mutation Models
Date: Fri, 10 Jun 2011 14:53:20 -0600
References: <972D673E3D084E2DBBD515DD90077C82@kenPC> <000001cc2606$b16669c0$14333d40$@com> <4DEFBCFF.6040501@gmail.com> <000001cc2610$d0ce1240$726a36c0$@com> <4DEFD211.60207@gmail.com> <000001cc26db$a4d9eb20$ee8dc160$@com> <4DF16E65.9050205@gmail.com><000001cc2745$06e43eb0$14acbc10$@com><4DF27CFB.10503@gmail.com>
In-Reply-To: <4DF27CFB.10503@gmail.com>


-----Original Message-----
From: David Johnston

Actually there is an
exact Bayesian solution to this problem.
Then for every possible tree, there are
variables for the length of time between each node. Then there are the
haplotypes for each node. That is a complete list of the parameters of
the complete likelihood.

Now if all you care about is the
Likelihood of the TMRCA between person A and B, you can get that by
marginalizing over all other parameters. In practice the number of
possible tree structures is enormous and so this is extrmely
computationally demanding even if you used Markov Chain Monte Carlo. But
it would be the optimal solution.

[[You can get most likely solution of the mutation outcome properties for a
given tree. To go further you have to introduce very subjective and
speculative assumptions from demographics about the relative probabilities
of all the different possible tree shapes. Every possible tree is certainly
not equally likely a-priori. So your problem is now a hybrid investigation
of mutations and demographics.

I think it better, or more grounded, to concentrate on interpreting
statistical property parameters of the seen mutations which result during
the tree unfolding and which are independent of speculative assumptions
about how to average over tree structures. This latter averaging attempt
could very well wash out the ability to learn about the tree structure ---
which usually is the goal of the enterprise. KN]]

This thread: