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<br>
There was a typically bad idea expressed on the R list today.<br>
<br>
<a class="moz-txt-link-freetext" href="https://stat.ethz.ch/pipermail/r-sig-mixed-models/2013q1/020017.html">https://stat.ethz.ch/pipermail/r-sig-mixed-models/2013q1/020017.html</a><br>
<br>
Ir reminded me of something I was thinking about a while back to
improve the<br>
performance of importing sampling for mixed models. The idea is to<br>
create negatively correlated random points. It is based on the
idea<br>
that for a std multivariate normal vector, the norm has a
probability<br>
density function <br>
<br>
c * r^{n-1} exp(-r^2/2)<br>
<br>
for a constant c.<br>
In general this produces a CDF based on the gamma function.<br>
The idea is to generate a sample of multivariate normals and then so
scale them<br>
based on the inverse of the CDF. We then restrict each one to the
shell<br>
based on its norm and maximize the distance between them all.<br>
For 2 dimensions one can plot the results. Here are 250 bivariate
normals.<br>
You can see that some of them are almost on top each other. This
produces<br>
inefficient sampling.<br>
<br>
<img src="cid:part1.05020402.04000007@otter-rsch.com" alt=""><br>
<br>
Now here are the results of rescaling the norms<br>
<br>
<img src="cid:part2.00030205.04050507@otter-rsch.com" alt=""><br>
and finally what we get after maximizing the distance between them.<br>
<br>
<img src="cid:part3.05070904.09010403@otter-rsch.com" alt=""><br>
<br>
Of course one does not need to use the inverse of the CDF based on
the normal.<br>
a fatter tailed distribution could be used. <br>
<br>
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