Systematic Error Parameter#
In some cases the data errors are underestimated. MICA can add a systematic error parameter to augment the data errors. MICA parameterizes the systematic error as
where \(\sigma_{\rm sys}\) is the systematic error and \(\sigma_{\rm data, mean}\) is the mean of the data errors, defined as
where \(\sigma_i\) is the data error of the \(i^{\rm th}\) data point and \(N\) is the number of data points.
MICA outputs the parameters list in the file data/para_names_line.txt_xx, where xx represents the number of components used. This file looks like:
0 sys_err_con LOGUNI 0.000000 0.000000 1 0.000000e+00
1 sigmad LOG -4.184615 -3.473817 0 -1.797693e+308
2 taud LOG 0.000000 7.359338 0 -1.797693e+308
3 sys_err_line LOGUNI 0.000000 2.397895 1 0.000000e+00
4 0-th_component_amplitude LOG -11.512925 2.302585 0 -1.797693e+308
5 0-th_component_center UNI 0.000000 100.000000 0 -1.797693e+308
6 0-th_component_sigma LOG -1.609438 4.422849 0 -1.797693e+308
As the name indicates, the 0th and 3rd parameters are the systematic error parameters for the continuum and line datasets, respectively. Then one gets the posterior samples of these parameters from the file data/posterior_sample1d.txt_xx. For example, with Python, one can do as follows
import numpy as np
sample = np.loadtxt('data/posterior_sample1d.txt_1')
err_con_mean = np.mean(con_data_err[:]) # Mean of data errors for continuum
err_line_mean = np.mean(line_data_err[:]) # Mean of data errors for line
sys_err_con = (np.exp(sample[:, 0])-1.0) * err_con_mean # Systematic error of continuum
sys_err_line = (np.exp(sample[:, 3])-1.0) * err_line_mean # Systematic error of line
print('Systematic error of continuum:', sys_err_con)
print('Systematic error of line:', sys_err_line)