CODEWITHSUNDEEP
pythonnumpyscipycurve-fittingscipy-optimize
George
George

Reputation: 451

Why are the errors so large?

I am trying to fit a power law of the form a*x**b+c to some data points, using curve_fit from scripy.optimize. Here's the MWE:

import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

def func_powerlaw(x, m, c, c0):
    return c0 + x**m * c

x = np.array([1.05, 1.0,  0.95, 0.9,  0.85, 0.8,  0.75, 0.7,  0.65, 0.6,  0.55])
y = np.array([1.26, 1.24, 1.2,  1.17, 1.1,  1.01, 0.95, 0.84, 0.75, 0.71, 0.63])
dy = np.array([0.078]*11)

fig, (a1) = plt.subplots(ncols=1,figsize=(10,10))
a1.errorbar(x, y, yerr = dy, ls = '', marker='o')

popt, pcov = curve_fit(func_powerlaw, x, y, sigma = dy, p0 = [0.3, 1, 1], bounds=[(0.1, -2, -2), (0.9, 10, 2)], absolute_sigma=False, maxfev=10000, method = 'trf')
perr=np.sqrt(np.diag(pcov))

xp = np.linspace(x[0],x[-1], 100)
a1.plot(xp, func_powerlaw(xp, *popt), lw=3, zorder = 1, c = 'b')
print(popt, perr)

Output: [0.35609897 3.24929422 -2.] [0.47034928 3.9030258 3.90965249]

Here's the Figure.

For all three parameters, the errors are larger than the value estimations themselves. Judging from experience this cannot be right, since the line fits the data points very well. Even if I don't set any bounds and/or initial guess, the values change, but the errors remain too high. The only boundary required is that 0.1<=m<=0.9. What am I doing wrong? Any help is greatly appreciated!

Upvotes: 3

Views: 1770

Answers (1)

Conor
Conor

Reputation: 1088

The size of the errors in your fit parameters is partly driven here by the size of the measurement errors (dy in your code). As you can see in the plot the sigmas are large relative to the dispersion of the points, so a wide range of curves could fit the data. The dy values are hard coded here, are they real values? Try making the smaller and see how that affects the curve fit errors. Also they look like absolute sigmas in the plot, so you should set the absolute_sigma flag to True.

As an added note, if you don't supply measurement errors in the sigma parameter the default is 1.0 (very large in your case) and not 0.0 for every y value. This explains why omitting sigma gives larger fit errors.

Upvotes: 2

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