Hi all,

I'll preface this with saying I've gone through the archives, and am still in 
need of some help.

I've been using this likelihood model with mean = 0 and s.d. = sqrt( (c + ( 1 / 
N1 ) + ( 1 / N2 ) ) * x * ( 1 - x )), where c is a genetic drift parameter 
(usually very small, like between .005 - .001), N1 and N2 are my population 
sizes (~200), and x is a value between 0 and 1. The values I'm testing are 
usually between -.25 to .25, so my command looks like

dnorm(.1, 0, sqrt( (c + ( 1 / N1 ) + ( 1 / N2 ) ) * x * ( 1 - x )))

Originally, I was doing this over multiple data points at once, summing up the 
values I was going to test and their variances, and just running the likelihood 
on these summed values once (getting one final likelihood in return). I've 
recently switched this over to running the likelihood on each data point and 
its associated variance one at a time, and summing the likelihoods afterwards. 
However, upon doing this, I'm now getting positive likelihoods since the 
individual variances are so small (.01 to .09, for instance). I'm not sure what 
to do, because I think these small variances are messing up the behavior of my 
final data -- the patterns I'm getting are not what I expected, whereas my 
previous method of summing multiple data points and just taking one likelihood 
value did return what I expected.

I'm not sure if getting positive likelihoods somewhat implies that the behavior 
of the model / results are off. Should I be using a different function than 
dnorm, now that my variances are so small? Using pnorm instead returns my data 
to what's expected, but my understanding is that pnorm gets me a probability 
now, not a likelihood. Could I use the output from pnorm in a likelihood ratio 
test (which was my original plan)?

Thanks for any help,
~Michael Turchin
Children's Hospital Boston
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