satlas.stats.fitting.create_band

satlas.stats.fitting.create_band(f, x, x_data, y_data, yerr, xerr=None, method='chisquare', func_chi=None, func_llh=<function poisson_llh at 0x0000000008DF2D08>, kind='prediction')

Calculates prediction or confidence bounds at the 1 level. The method used is based on the Delta Method: at the requested prediction points x, the bound is calculated as

with G the cost function, H the Hessian matrix and the vector of parameters. The resulting bound needs to be subtracted and added to the value given by the model to get the confidence interval.

For a prediction interval, the value before taking the square root is increased by 1

Parameters:

• f (BaseModel) – Model for which the bound needs to be calculated.
• x (array_like) – Selection of values for which a prediction needs to be made.
• x_data (array_like) – Experimental data for the x-axis.
• y_data (array_like) – Experimental data for the y-axis.
• yerr (array_like) – Experimental uncertainty for the y-axis.
• xerr (array_like) – Experimental uncertainty for the x-axis. Defaults to None.
• method ({'mle', 'chisquare'}) – Selected method for which the cost function is selected.
• func_chi (function, optional) – Is passed on to the chisquare methods in order to calculate the experimental uncertainty from the modelvalue. Defaults to None, which uses yerr.
• func_llh (function) – Is passed on to the likelihood fitting method to define the likelihood function. Defaults to satlas.loglikelihood.poisson_llh.
• kind ({'prediction', 'confidence'}) – Selects which type of bound is calculated.

Returns:

bound – Array describing the deviation from the model value as can be expected for the selected parameters at the 1:math:sigma level.

Return type:

array_like