在scipy.optimize.curve_fit中使用absolute_sigma参数

Question

为了执行合适,我目前正在使用curve_fitfrom scipy.optimize.

我已经计算了与我的每个相关的错误ydata,我想将sigma = y_errors数据中计算出的当前值添加到拟合中,

即最小化sum( ((f(xdata, *popt) - ydata) / sigma)**2 )而不是仅仅sum( (f(xdata, *popt) - ydata)).

我可以看到可以sigma在文档中分配参数.我不清楚的是absolute_sigma参数.文档中给出的解释对我来说很混乱.

我应该设置absolute_sigma= = True吗？或者它应该设置为False如果我需要考虑y_errors与我的每一个相关联ydata？

Answer 1

如果您的数据存在绝对不确定性，即如果您的单位与您的单位y_errors相同ydata，那么您应该设置absolute_sigma= = True。然而，通常情况下，单位y_errors不准确，只有相对大小是已知的。后一种情况的一个例子可能是某些y值来自相同x值的重复测量。然后将重复y值的权重设为非重复值的两倍是有意义的y，但此权重 ( 2) 的单位与任何单位不同y。

下面是一些代码来说明差异：

import numpy as np
from scipy.optimize import curve_fit
from scipy.stats import norm

# defining a model
def model(x, a, b):
    return a * np.exp(-b * x)

# defining the x vector and the real value of some parameters
x_vector = np.arange(100)
a_real, b_real = 1, 0.05

# some toy data with multiplicative uncertainty
y_vector = model(x_vector, a_real, b_real) * (1 + norm.rvs(scale=0.08, size=100))

# fit the parameters, equal weighting on all data points
params, cov = curve_fit(model, x_vector, y_vector )
print params
print cov


# fit the parameters, weighting each data point by its inverse value
params, cov = curve_fit(model, x_vector, y_vector, 
                        sigma=1/y_vector, absolute_sigma=False)
print params
print cov

# with absolute_sigma=False:
## multiplicative transformations of y_data don't matter
params, cov = curve_fit(model, x_vector, y_vector, 
                        sigma=100/y_vector, absolute_sigma=False)
print params
print cov

# but absolute_sigma=True:
## multiplicative transformations of sigma carry through to pcov
params, cov = curve_fit(model, x_vector, y_vector,
                        sigma=100/y_vector, absolute_sigma=True)
print params
print cov

[ 1.03190409  0.05093425]
[[  1.15344847e-03   5.70001955e-05]
 [  5.70001955e-05   5.92595318e-06]]

[ 1.0134898   0.04872328]
[[  1.57940876e-04   1.56490218e-05]
 [  1.56490218e-05   3.56159680e-06]]

[ 1.0134898   0.04872328]
[[  1.57940878e-04   1.56490220e-05]
 [  1.56490220e-05   3.56159682e-06]]

[ 1.0134898   0.04872328]
[[ 2978.10865352   295.07552766]
 [  295.07552766    67.15691613]]