Hi -- your help with this would be much appreciated:
Imagine I have a set of multivariate (mean normalised) observations, {x}.
One can easily perform Principal Component Analysis to find a
transformation matrix P, such that x~=Pb, where b is the parameterisation
of x in the PC space (i.e. x is approximated by Pb, if we drop the dims
that account for low variance).
Further, imagine that my data set {x} forms a multivariate normal
distribution in the PC space -- i.e. {b} is distributed normally. (This is
not a wild assumption in my situation). I know the mean vector b_mean and
covariance matrix, C, (both in the PC space).
Now, suppose that I want to sample from this normal distribution and that
I have some constraints in the original data space (but not necessarily
all of them). (For example I know the values of x_1, x_3 and x_10.) I
want to be able to apply these constraints in the PC space and have a
way to sample from this conditioned distribution in the PC data space,
such that when I project the sample back into the original data space, the
constraints imposed in that space are met.
I'm no statistician -- your help is greatly appreciated.
.
.
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