Log-likelihood discrepancy between Felsenstein & Stamatakis ascertainment bias corrections

[Asif]

Dear Alexis & co.

I've noticed a strange discrepancy in the ascertainment bias correction when comparing results from 'felsenstein' and 'stamatakis' corrections.

For simplicity, assume JC69 model and no site rate variation:

-m ASC_GTRCAT --JC69 -V

I create a partition file, e.g.:

[asc~mc.v.paml.inv], ASC_DNA, p1=1-300

For the 'felsenstein' correction, I set the total number of constant sites in mc.v.paml.inv:

200

For the 'stamatakis' correction, I can specify the nucleotide freq. of constant sites:

50 50 50 50

Using the values above, both the felsenstein and stamtakis corrections should give the same log-likelihood, but they don't seem to.

I get:

felsenstein correction lnl = -1643.503274

stamatakis correction lnl = -1920.762146

The MLE tree and branch lengths are identical. I've attached the relevant files. I compiled from source (download from Github 16/6/16) on OSX. The commands I use to run:

echo "200" > mc.v.paml.inv; raxmlHPC-AVX -m ASC_GTRCAT --JC69 -V -n test_fels -q mc.v.paml.part --asc-corr=felsenstein -p 54321 -s mc.v.paml

and

echo "50 50 50 50" > mc.v.paml.inv; raxmlHPC-AVX -m ASC_GTRCAT --JC69 -V -n test_stams_50_50 -q mc.v.paml.part --asc-corr=stamatakis -p 54321 -s mc.v.paml

(I get the same result using -m ASC_GTRGAMMA --JC69)

Am I right in thinking the log-likelihoods should be the same?

Kind regards,

Asif

[Alexandros Stamatakis]

Dear Asif,

I don't think that the likelihoods should be the same, please have a
look at the maths supplement of the respective paper (attached).

The Felsenstein correction is:

the standard log likelihood + w * log(L(A) + L(C) + L(G) + L(T)) where w
:= 200 in your example,

my correction is:

standard log likelihod + w/4 * log(L(A)) + ... + w/4 * log(L(T))

where w/4 := 50 in your example

Alexis

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--
Alexandros (Alexis) Stamatakis

Research Group Leader, Heidelberg Institute for Theoretical Studies
Full Professor, Dept. of Informatics, Karlsruhe Institute of Technology
Adjunct Professor, Dept. of Ecology and Evolutionary Biology, University
of Arizona at Tucson

www.exelixis-lab.org

[Asif]

Thank you for clarifying, Alexis. I misunderstood what your correction was doing.

Hope all else is well.

Asif