[SciPy-User] How to fit data obtained from a Monte Carlo simulation?

josef.pktd@gmai... josef.pktd@gmai...
Thu Sep 22 11:21:23 CDT 2011


On Thu, Sep 22, 2011 at 11:50 AM, D K <canavanin@yahoo.se> wrote:
> Dear David
>
> thank you very much for your reply. I have been playing around with
> fmin's ftol and xtol arguments, as you suggested. It's looking promising
> so far, but then my initial guesses have been rather close to the true
> values of my test set. I will keep testing, and maybe write to the
> mailing list again at some point. Thanks again!

If the problem is the MonteCarlo noise, then the question is whether
you keep a fixed random.seed during the calculations?

If you have a fixed seed, then you have the same MonteCarlo noise in
all calculations and it shouldn't affect the derivative calculations
or the calculations for different parameters.

Josef

>
> /Donata
>
>
> PS: Also thanks very much to Josef, who also replied to my email. I will
> keep trying a bit with fmin and its parameters at first, and answer your
> questions in case I still don't get anywhere this way. I hope this
> approach is ok...
>
>
> On 09/21/2011 09:20 PM, J. David Lee wrote:
>> On 09/21/2011 09:47 AM, D K wrote:
>>> Hi everyone
>>>
>>> I would like to fit data obtained from a Monte Carlo simulation to
>>> experimental data, in order to extract two parameters from the
>>> experiments. There are several issues with this:
>>>
>>> a) There is a small element of randomness to each simulated data point;
>>> we don't actually have a function describing the curve (the overall
>>> curve shape is reproducible though).
>>> b) I have never performed curve fitting before, and I haven't got a clue
>>> how to even go about looking for the required information.
>>> b) I don't have a strong maths background.
>>>
>>> I tried using optimize.leastsq, but I learnt that, apparently, I ought
>>> to know the function describing my data to be able to use this (I kept
>>> researching, as it exited with code 2, claiming that the fit had been
>>> successful, but it mainly returned the initial guess as the fitting
>>> result). So I switched to optimize.fmin (having read that it only uses
>>> the function values); this, however, does not converge and simply exits
>>> after the maximum number of iterations have been performed.
>>>
>> Hi Donata,
>>
>> Because your model varies from run to run, you may not be able to reach
>> the default tolerances necessary for successful termination of leastsq.
>> If you look at the documentation for leastsq, you will see several
>> tolerance parameters, ftol, xtol, and gtol. Modifying these may help in
>> your case.
>>
>> Most (all?) of these optimization routines are doing some kind of
>> gradient descent. The variability in your model will affect both the
>> error estimate and the search direction. Because you'll be calculating
>> the Jacobian matrix (gradients) numerically, you're almost certainly
>> want to modify leastsq's epsfcn parameter. Using the default value, it
>> may be that the variability in your model will be larger than the
>> difference due to the delta x used. In that case, your search direction
>> could be essentially random.
>>
>> After writing this, I'm thinking that fmin would be a better fit, as it
>> doesn't have the numerical gradient calculation and associated problems.
>> fmin has the same xtol and ftol arguments as leastsq that might be useful.
>>
>> David
>>
>>
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