[Taxacom] Markov chain Monte Carlo

Richard Zander Richard.Zander at mobot.org
Thu Apr 19 10:29:58 CDT 2012


Carl:
I much appreciate the clear short response. I was wrong to use "tree."
And also "clade" is wrong in place of "tree" since one is not looking
for the "best" clade but the one that appears most often.

Yes, each tree must be improbable (multiply the posterior probabilities
of each branch to get the probability of the entire tree). 

So when the posterior is given as 0.95, it means that branch
configuration (clade) appears 0.95 of the time in the sample, which if
large enough implies that it also appears 0.95 of the time in the
unsampled population.

Dang. 

Many thanks,
Richard

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Richard H. Zander
Missouri Botanical Garden, PO Box 299, St. Louis, MO 63166-0299 USA  
Web sites: http://www.mobot.org/plantscience/resbot/ and
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-----Original Message-----
From: Carl Rothfels [mailto:crothfels at yahoo.ca] 
Sent: Wednesday, April 18, 2012 5:45 PM
To: Richard Zander
Subject: Re: [Taxacom] Markov chain Monte Carlo
Very short superficial response -- your initial description of MCMC is
correct -- it attempts to sample from the posterior distribution in
proportion to its probability density. But you're going astray when you
start thinking about there being one tree that has a .95 posterior -- in
any dataset with more than a handful of taxa any single tree will have
an extremely low posterior (which may be what you're trying to say). In
fact, with many taxa, the chances of sampling any tree even twice is
low, even if you take very many samples from the posterior. So that's
why folks concentrate on elements of the posterior, rather than on
complete trees -- in what proportion of the sample is a given split in
the tree supported (the posterior support for that branch)? What's the
average length of this branch in the posterior? etc. The presence of a
huge number of unique and extremely unlikely trees doesn't affect these
measures (not in a way that is not already captured by the MCMC,
provided the MCMC has sampled the posterior well, as it should if the
researchers did a good job..).

carl rothfels




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