# [SciPy-User] Confidence interval for bounded minimization

Christopher Jordan-Squire cjordan1@uw....
Wed Feb 22 23:09:57 CST 2012

```On Wed, Feb 22, 2012 at 2:02 PM, Nathaniel Smith <njs@pobox.com> wrote:
> On Wed, Feb 22, 2012 at 8:48 PM,  <josef.pktd@gmail.com> wrote:
>> On Wed, Feb 22, 2012 at 3:26 PM, Greg Friedland
>> <greg.friedland@gmail.com> wrote:
>>> Hi,
>>>
>>> Is it possible to calculate asymptotic confidence intervals for any of
>>> the bounded minimization algorithms? As far as I can tell they don't
>>> return the Hessian; that's including the new 'minimize' function which
>>> seemed like it might.
>>
>> If the parameter ends up at the bounds, then the standard statistics
>> doesn't apply. The Hessian is based on a local quadratic
>> approximation, which doesn't work if part of the local neigborhood is
>> out of bounds.
>> There is some special statistics for this, but so far I have seen only
>> the description how GAUSS handles it.
>>
>> In statsmodels we use in some cases the bounds, or a transformation,
>> just to keep the optimizer in the required range, and we assume we get
>> an interior solution. In this case, it is possible to use the standard
>> calculations, the easiest is to use the local minimum that the
>> constraint or transformed optimizer found and use it as starting value
>> for an unconstrained optimization where we can get the Hessian (or
>> just calculate the Hessian based on the original objective function).
>
> Some optimizers compute the Hessian internally. In those cases, it
> would be nice to have a way to ask them to somehow return that value
> instead of throwing it away. I haven't used Matlab in a while, but I
> remember running into this as a standard feature at some point, and it
> was quite nice. Especially when working with a problem where each
> computation of the Hessian requires an hour or so of computing time.
>

hessians? I'd assumed that anything derived from finite difference
estimations wouldn't give particularly good confidence intervals, but
I've never needed them so I've never looked into it in detail.

-Chris

> -- Nathaniel
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```