并非始终显示lmfit参数上的错误

Question

I am trying to fit a curve to some data points using lmfit and I need the errors on the parameters. After I call: out = model.fit(y, pars, x, weights = 1/error) I do: print(out.fit_report()) . Sometimes the output is like this (part of hit posted here):

# fitting method   = leastsq
    # function evals   = 490
    # data points      = 380
    # variables        = 14
    chi-square         = 1035.65572
    reduced chi-square = 2.82966043
    Akaike info crit   = 408.995142
    Bayesian info crit = 464.157539
[[Variables]]
    line1_c:        49.2699229 +/- 0.17590656 (0.36%) (init = 60.38407)
    sv1_skew:      -6.04992639 +/- 0.50325827 (8.32%) (init = 0)
    sv1_center:     13284.8621 +/- 0.01423913 (0.00%) (init = 13284)
    sv1_sigma:      1.32758560 +/- 0.02864233 (2.16%) (init = 1)
    sv1_amplitude:  240.685241 +/- 3.80236837 (1.58%) (init = 1)
    sv1_gamma:      1.32758560 +/- 0.02864233 (2.16%) == 'sv1_sigma'

which is what I need (ie the parameters have errors associated with them). However other times it is like this:

    # fitting method   = leastsq
    # function evals   = 9509
    # data points      = 64
    # variables        = 14
    chi-square         = 3023.19802
    reduced chi-square = 60.4639605
    Akaike info crit   = 274.731995
    Bayesian info crit = 304.956358
##  Warning: uncertainties could not be estimated:
    sv3_center:     at initial value
    sv4_amplitude:  at boundary
[[Variables]]
    line1_c:        49.6633100 (init = 60.35763)
    sv1_skew:      -19.2947984 (init = 0)
    sv1_amplitude:  269.063100 (init = 1)
    sv1_center:     13285.0635 (init = 13284)
    sv1_sigma:      1.66532381 (init = 1)
    sv1_gamma:      1.66532381 == 'sv1_sigma'

Why can't the uncertainties be estimated in the second case. Also, for the exactly same fit and data, sometimes I get the errors on parameters, sometimes I don't ie I just run python code.py twice in a row, without any modification, and sometimes I get the estimates of the error sometimes I don't. However in both cases the fit looks really good by eye. Can someone help me understand what is going on? Thank you!

Answer 1

If one or more of the variables does not cause a change in the fit result, the uncertainties in the parameter values cannot be estimated. This most often means that one or more of the Parameters is stuck at an initial value (perhaps a very poor guess, or perhaps cause part of the model to be unresponsive) or stuck at a boundary.

The fit report tries to give some good hints about what is preventing the uncertainties from be estimated. It says:

##  Warning: uncertainties could not be estimated:
    sv3_center:     at initial value
    sv4_amplitude:  at boundary

Among other things, this means you did not include the full error report, which would have listed all 14 variables.