Fitresults

The fitresults objects is a pretty straightforward collection of fitresults.

Note that all results are purely based on the fitting and do not include model uncertainties from e.g. the linelist.

The given uncertainties in punc are estimated from the residual distribution and seem to be reasonable for some parameters, but get problematic if the parameter only affects a small number of points (e.g. individual abundances).

Here are the fields

maxiter:

Maximum number of iterations

chisq:

Final chi square

uncertainties:

Uncertainties of the fitparameters bases on SME statistics

fit_uncertainties:

Uncertainties of the fitparameters based solely on the least-squares fit

covar:

covariance matrix of the fitparameters

grad:

the gradient of the cost function for each parameter

pder:

The jacobian, i.e. the derivate at each point for each parameter

resid:

The residual between observation and model

Uncertainties

As mentioned above we estimate the uncertainties using a special metric. This metric is based on the destribution of the derivatives for each fitparameter. We estimate the cumulative distribution function of the generalized normal distribution with:

x = residual / derivate
y = abs(derivate) / uncs
y = cumulative_sum(y)
#normalize
y /= y[-1]

(Example of the cumulative distribution function for various values of sigma)

It is explained in detail in Paper II (SME: Evolution)