Re: Help setting up an array

[Peter Thorne <peter.thorne(at)uea.ac.uk>]

Jaco van Gorkom wrote:
 
> Just out of curiosity: did you create this little puzzle just to test
> our
> brain cells, or is there a real-world application for this problem?

It is a real world problem, believe it or not! We have a number of
observational parameters which we wish to regress against possible
modelled causes in a system containing "noise". Output from this
regression is effectively a cloud of potential solution points, an
n-dimensional PDF (probability density function) ellipsoid. Previously
we have only considered ellipsoids as single pieces of data. However, in
this system we wish to assess the consistency of the model system and
therefore need to intercompare m n-dimensional ellipsoids (where m
distinct realisations are made through the regression analysis).
Effectively we need to set up a system whereby the null hypothesis is
that all m fields gained are equivalent (are sub-sampled from some true
population). To gain a quantitative measure of this statistic it is
required to integrate the fields over the n-dimensional phase space
which is common to the m fields and gain the maximum probability
function from the m fields for this integral. Maximum because the
ellipsoids are not expected to have equal variance, distributions or
orientation in the regression phase space.

Well, you did ask ...