[AstroPy] Chi-square problems with lmfit and scipy

[Rudolf Baer]

I am fitting the continuum of a NIR spectrum with a blackbody plus power
law using lmfit and scipy. The plot of the fit looks good
and the resulting parameters agree reasonably with previous results.

T:      1109.29505 +/- 3.08340774 (0.28%) (init = 1100)
const:  4.7240e-21 +/- 6.3014e-23 (1.33%) (init = 2e-21)
A:      2.4188e-11 +/- 6.3181e-14 (0.26%) (init = 2e-11)
p:     -1.06704890 +/- 0.01701493 (1.59%) (init = -1)

However the chi-square and reduced chi-square values
(chi-square = 1.1268e-20 reduced chi-square = 2.1039e-24)
are clearly wrong. The problem is apparently known as the scipy guide says*
Note that the calculation of chi-square and*
*reduced chi-square assume that the returned residual function is scaled
properly to the uncertainties in the data. *

*For these statistics to be meaningful, the person writing the function to
be minimized must scale them properly.*
 I do not know how to do this. Any advice will be appreciated.

With kind regards
Rudolf Baer
Zurich



The input data for the code are x: lambda in AA, y: flux density in
erg/cm^{2}/s/{\AA)
Code:

x=x_AA/10000. #<---------conversion AA to um

y=y*1e4

y=y*x
#=========================================================================================

def bb(x, T, const):

    from scipy.constants import h,k,c

    x = 1e-6 * x # convert to metres from um

    return const*2*h*c**2 / (x**5 * (np.exp(h*c / (x*k*T)) - 1)) #J/s/m2/m


def powerlaw(x,A,p):

    return A*x**p


mod= Model(bb) + Model(powerlaw)

pars  = mod.make_params(T=1100,const=2*1e-21,A=2*1e-11,p=-1.0)

 result = mod.fit(y,pars,x=x)
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