Hi Dean.
It seems to me that what you've identified is a trend towards an
increase in the absolute value of the mean with increased sigma^2?
This is indeed a robust pattern, but it has nothing to do with any trend
or bias - it is just due to the fact that the sampling variance of the
phylogenetic mean increases in direct proportion to the evolutionary
rate under Brownian motion.
In the limiting case this becomes obvious, right? Imagine if sigma^2 is
set to zero:
> X0<-fastBM(tree,sig=0,nsim=10000)
> mean(X0)
[1] 0
Your simulation is the same as drawing sets of random values from the
normal with difference variances and computing the absolute value of
their means (you've done this many times, but the effect is the same).
As long as the sample is finite, and the same for each simulated
variance, the result is a strong pattern of increasing absolute value of
the mean for increased variance in the simulated distribution.
Try this to see what I mean:
xbar<-vector()
for(i in -5:5) xbar[i+6]<-abs(mean(rnorm(n=1000,sd=(10^i)^2)))
plot(10^c(-5:5),xbar,log="xy")
Sincerely, Liam
--
Liam J. Revell
University of Massachusetts Boston
web: http://faculty.umb.edu/liam.revell/
email: liam.rev...@umb.edu
blog: http://phytools.blogspot.com
On 5/20/2011 5:40 PM, Dean Adams wrote:
Hi Luke,
The bit where I noticed it would be in the 'meanmeans' in your code.
Deviation from zero is ~ 6e-5 for rate = 0.001, and increases to 1.1e-1
as rate goes to 1000. True it is slight, but this pattern mimics what I
observed.
meanmeans
[1] -6.856330e-05 -7.238577e-05 2.534556e-03 -2.602753e-03 7.473694e-03
[6] -1.020982e-02 1.116674e-01
But it is quite true that the distribution of individual simulation
means appears centered around zero for all cases (and relative to the
distribution of individual outcomes, the 'meanmeans' trend is very small).
Thanks,
Dean
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