plot_pvalue

Context: plotting

Synopsis

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

Syntax

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)

Description

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>

Examples

Example 1

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)

Example 2

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)

Example 3

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

Changes in CIAO

Changed in CIAO 4.17

The "wstat" statistic can now be used with this routine.

Bugs

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