[Numpy-discussion] Ticket #1223...
David Goldsmith
d.l.goldsmith@gmail....
Thu Jul 1 12:43:50 CDT 2010
On Thu, Jul 1, 2010 at 9:11 AM, Charles R Harris
<charlesr.harris@gmail.com>wrote:
>
> On Thu, Jul 1, 2010 at 8:40 AM, Bruce Southey <bsouthey@gmail.com> wrote:
>
>> On 06/29/2010 11:38 PM, David Goldsmith wrote:
>>
>> On Tue, Jun 29, 2010 at 8:16 PM, Bruce Southey <bsouthey@gmail.com>wrote:
>>
>>> 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
>>> >
>>> > _______________________________________________
>>> > 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.")
>>
>> DG
>>
>> >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
>> _______________________________________________
>> NumPy-Discussion mailing list
>> NumPy-Discussion@scipy.org
>> http://mail.scipy.org/mailman/listinfo/numpy-discussion
>>
>>
>>
>> --
>> 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)
>>
>>
>> _______________________________________________
>> NumPy-Discussion mailing listNumPy-Discussion@scipy.orghttp://mail.scipy.org/mailman/listinfo/numpy-discussion
>>
>> As you (and the theory) say, a variance should not be negative - yeah
>> right :-) In practice that is not exactly true because estimation procedures
>> like equating observed with expected sum of squares do lead to negative
>> estimates. However, that is really a failure of the model, data and
>> algorithm.
>>
>> I think the issue is really how numpy should handle input when that input
>> is theoretically invalid.
>>
>>
> I think the svd version could be used if a check is added for the
> decomposition. That is, if cov = u*d*v, then dot(u,v) ~= identity. The
> Cholesky decomposition will be faster than the svd for large arrays, but
> that might not matter much for the common case.
>
> <snip>
>
> Chuck
>
Well, I'm not sure if what we have so far implies that consensus will
possibly be impossible to reach, so I'll just rest on my laurels (i.e., my
proposed compromise solution); just let me know if the docstring needs to be
changed (and how).
DG
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