[SciPy-User] Confidence interval for bounded minimization

josef.pktd@gmai... josef.pktd@gmai...
Wed Feb 22 14:48:37 CST 2012

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).


> Thanks.
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