On Tue, Jun 29, 2010 at 6:03 PM, David Goldsmith <d.l.goldsmith@gmail.com> wrote:

On Tue, Jun 29, 2010 at 3:56 PM, <josef.pktd@gmail.com> wrote:

On Tue, Jun 29, 2010 at 6:37 PM, David Goldsmith <d.l.goldsmith@gmail.com> wrote:

...concerns the behavior of numpy.random.multivariate_normal; if that's 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

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As I recall, there is no requirement for the variance/covariance of the normal distribution to be positive definite.

From http://en.wikipedia.org/wiki/Multivariate_normal_distribution "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. Bruce