[SciPy-User] lmfit: confidence intervals issue

[Antonino Ingargiola]

Hi Matt,


On Fri, Jun 20, 2014 at 2:12 PM, Matt Newville <newville at cars.uchicago.edu>
wrote:
[cut]

>  Thanks for the explanation, now I understand much better the problem. I
>> have a model function with a discontinuity in the origin (i.e. exp(-x - x0)
>> for x > x0 else 0). If I sample it with a step dx, I will always have a
>> problem when x0 changes less than dx. Is there any known trick I can use to
>> avoid this problem?
>>
>
> I'm not sure that there is a robust way to have the range of data
> considered in the fitting to be a parameter.  I might suggest (but haven't
> looked at your situation in great detail) to have you consider using an
> "offset" that shifts the origin for the model, then interpolate that onto
> the grid of data.  That way, you might be able to set a fit range in the
> data coordinates before the fit, and not have it change.  The model can be
> shifted in "x" (assuming there is such a thing -- your data appears to have
> an obvious "x" axis), but is fitting a fixed data range.  Again, I'm not
> sure that would fix all problems, but it might help.
>

Unless I misunderstood, I do already what you suggest. My function is exp(-
x + x0) (note that I wrote "-x0" before by mistake) and x0 is "continuous",
regardless of the x discretization. The problem is that the function is 0
for x < x0 and therefore there is a discontinuity at x=x0. When the
function is evaluated on the save discrete x arrays, changing smoothly x0
does not result in a smooth translation of the function.


>
>
>> In short, it's a challenge to  have variables that are used essentially
>> as integers.  Still, even if it doesn't work well, it shouldn't be failing
>> this way.
>>
>
>  Yes, but now I'm curious. How did you get around the problem?
>>
>
> Least-squares fitting with values used as integers are going to have
> poorly defined derivatives, and are bound to cause problems, at least
> sometimes.  I don't know of a general solution, but perhaps someone does.
>

I think that fitting a function with a discontinuity using an offset (x
translation) as a parameter should be a quite common problem.

Now that I think about this, maybe, constraining the offset variable within
a single step of x will result in a smooth behavior and would allow to find
the offset with accuracy of a fraction of the discretization step. I'll
try...

Thinking loud, would be nice to have a 2-step fit. In step 1, you find the
offset varying it with the same discretization of the x axis. In the second
step, you vary the offset only within one x bin to find the fractional part.

Does this makes sense? Any idea if would it be feasible with current
lmfit/scipy?

Thanks,
Antonio
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