[Numpy-discussion] Ticket #1223...
Tue Jun 29 23:38:23 CDT 2010
On Tue, Jun 29, 2010 at 8:16 PM, Bruce Southey <firstname.lastname@example.org> wrote:
> On Tue, Jun 29, 2010 at 6:03 PM, David Goldsmith
> <email@example.com> wrote:
> > On Tue, Jun 29, 2010 at 3:56 PM, <firstname.lastname@example.org> wrote:
> >> On Tue, Jun 29, 2010 at 6:37 PM, David Goldsmith
> >> <email@example.com> wrote:
> >> > ...concerns the behavior of numpy.random.multivariate_normal; if
> >> > of
> >> > interest to you, I urge you to take a look at the comments (esp. mine
> >> > :-) );
> >> > otherwise, please ignore the noise. Thanks!
> >> You should add the link to the ticket, so it's faster for everyone to
> >> check what you are talking about.
> >> Josef
> > Ooops! Yes I should; here it is:
> > http://projects.scipy.org/numpy/ticket/1223
> > Sorry, and thanks, Josef.
> > DG
> > _______________________________________________
> > NumPy-Discussion mailing list
> > NumPy-Discussion@scipy.org
> > http://mail.scipy.org/mailman/listinfo/numpy-discussion
> As I recall, there is no requirement for the variance/covariance of
> the normal distribution to be positive definite.
No, not positive definite, positive *semi*-definite: yes, the variance may
be zero (the cov may have zero-valued eigenvalues), but the claim (and I
actually am "neutral" about it, in that I wanted to reference the claim in
the docstring and was told that doing so was unnecessary, the implication
being that this is a "well-known" fact), is that, in essence (in 1-D) the
variance can't be negative, which seems clear enough. I don't see you
disputing that, and so I'm uncertain as to how you feel about the proposal
to "weakly" enforce symmetry and positive *semi*-definiteness. (Now, if you
dispute that even requiring positive *semi*-definiteness is desirable,
you'll have to debate that w/ some of the others, because I'm taking their
word for it that indefiniteness is "unphysical.")
"The covariance matrix is allowed to be singular (in which case the
corresponding distribution has no density)."
So you must be able to draw random numbers from such a distribution.
Obviously what those numbers really mean is another matter (I presume
the dependent variables should be a linear function of the independent
variables) but the user *must* know since they entered it. Since the
function works the docstring Notes comment must be wrong.
Imposing any restriction means that this is no longer a multivariate
normal random number generator. If anything, you can only raise a
warning about possible non-positive definiteness but even that will
vary depending how it is measured and on the precision being used.
NumPy-Discussion mailing list
Mathematician: noun, someone who disavows certainty when their uncertainty
set is non-empty, even if that set has measure zero.
Hope: noun, that delusive spirit which escaped Pandora's jar and, with her
lies, prevents mankind from committing a general suicide. (As interpreted
by Robert Graves)
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