# Parametric bootstrapping

Vijay Aswani aswaniv at naos.si.edu
Thu May 4 13:58:49 EST 2000

```Hi all,

First of all, I would like to thank all those who responded to my earlier
posting asking for information on parametric bootstrapping. They were Chris
Conroy, Andrew Rambaut, John Huelsenbeck, Thomas Buckley and Jack Sullivan.

A number of those who responded pointed me to the web site of Nick Goldman
who had a manuscript and some very helpful procedural tips on the process.

I am writing to report that I have carried out the process and ... have some
questions.

First of all, the procedure seems to call for simulating datasets (I used a
100 replications) using the null hypothesis tree and estimated likelihood
parameters of that tree. The null hypothesis tree, as I understand it, is
not the best ML tree but the hypothetical topology I wish to test (eg.
monophyly of a particular group).

Once I have the 100 datasets, I then calculate the ML score of the best tree
(by heuristic search) and the ML score of the hypothesis tree. I subtract:
Lnull - LML and plot the distribution of these 100 values.

I ran the test twice with 2 different hypotheses. I therefore simulated 100
datasets in each case. I noticed that in both of these results, the
difference in ML values between the ML score of the best tree and the null
hypothesis tree was very small. (As it turns out, in both cases, the
hypotheses were rejected because of a larger difference between the real
best ML score and null hypothesis ML score).

This brings me to my question: isn't using the hypothesis tree's topology
and ML parameters to build the 100 datasets and then computing the best tree
in each dataset a bit circular. Wouldn't the best tree in each case be the
same tree whose topology and ML parameters were used to create the data sets
in the first place? Perhaps the reason why L null and L ML differ so little
is that the dataset was created from the parameters of the null tree.

If this is true, then the range of L ml - L null would be very small (since
they would be almost the same) and almost every hypothesis tested would be
rejected.

I would appreciate any thoughts on this ...

thanks,

Vijay
________________________________________________
Vijay Aswani, Ph.D.
Smithsonian Tropical Research Institute,
Unit 0948
APO AA 34002-0948
U.S.A.
Tel: +507-212-8824
Fax: +507-212-8790
Email: aswaniv at naos.si.edu or vaswani at sinfo.net
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