    Compute and plot a histogram of likelihood ratios by simulating data.

plot_pvalue(null_model, alt_model, conv_model=None, id=1, otherids=(), num=500, bins=25, numcores=None, replot=False, overplot=False, clearwindow=True, **kwargs)
conv_model - optional
id - int or str, optional
otherids - sequence of int or str, optional
num - int, optional
bins - int, optional
numcores - optional
replot - bool, optional
overplot - bool, optional
clearwindow - bool, optional

Compare the likelihood of the null model to an alternative model by running a number of simulations to calibrate the likelihood ratio test statistics. The distribution of the simulated likelihood ratios is plotted and compared to the likelihoods of the two models fit to the observed data. The fit statistic must be set to a likelihood-based method, such as "cash" or "cstat". Screen output is created as well as the plot; these values can be retrieved with `get_pvalue_results` .

The algorithm is based on the description in Sec.5.2 in "Statistics, Handle with Care: Detecting Multiple Model Components with the Likelihood Ratio Test" by Protassov et al., 2002, The Astrophysical Journal, 571, 545; <doi:10.1086/339856>

Use the likelihood ratio to see if the data in data set 1 has a statistically-significant gaussian component:

>>> create_model_component('powlaw1d', 'pl') >>> create_model_component('gauss1d', 'gline') >>> plot_pvalue(pl, pl + gline)

Use 1000 simulations and use the data from data sets 'core', 'jet1', and 'jet2':

>>> mdl1 = pl >>> mdl2 = pl + gline >>> plot_pvalue(mdl1, mdl2, id='core', otherids=('jet1', 'jet2'), ... num=1000)

Apply a convolution to the models before fitting:

>>> rsp = get_psf() >>> plot_pvalue(mdl1, mdl2, conv_model=rsp)

PARAMETERS

The parameters for this function are:

Parameter
Definition
null_model
The model expression for the null hypothesis.
alt_model
The model expression for the alternative hypothesis.
conv_model
An expression used to modify the model so that it can be compared to the data (e.g. a PSF or PHA response).
id
The data set that provides the data. The default is 1.
otherids
Other data sets to use in the calculation.
num
The number of simulations to run. The default is 500.
bins
The number of bins to use to create the histogram. The default is 25.
numcores
The number of CPU cores to use. The default is to use all the cores on the machine.
replot
Set to True to use the values calculated by the last call to `plot_pvalue` . The default is False .
overplot
If True then add the data to an exsiting plot, otherwise create a new plot. The default is False .
clearwindow
Should the existing plot area be cleared before creating this new plot (e.g. for multi-panel plots)?

Notes

Each simulation involves creating a data set using the observed data simulated with Poisson noise.

For the likelihood ratio test to be valid, the following conditions must hold:

The null model is nested within the alternative model.
The extra parameters of the alternative model have Gaussian (normal) distributions that are not truncated by the boundaries of the parameter spaces.

See the bugs pages on the Sherpa website for an up-to-date listing of known bugs.

December 2023