Add p_astro likelihood

[shanikagalaudage]

Adds p_astro likelihood as described in Eq. (40) of https://arxiv.org/abs/1912.09708

[ColmTalbot]

@shanikagalaudage, thanks for adding this! I have a couple of comments/suggestions.

I kind of like the fiducial_vt argument, although would you mind renaming it fiducial_selection? This will be more in line with the selection_function arguments. Also, please can you move it to just before cupy=True. Ideally, people would use kwargs, but that isn't always the case.

Both the comment strings should make it clear that the sampling prior distribution is the fiducial model being used.

I think it's worth adding the following to the init and removing the helper method you added.

        self._log_fiducial_selection = xp.log(fiducial_selection)

If we add this attribute to the likelihood, we should use it. I would suggest modifying _get_selection_factor in the HyperparameterLikelihood to use VT(Lambda) / VT(fiducial) rather than just VT(Lambda). I think we should leave the rate version as is, as that has a physical meaning.

Similarly, unless there's a reason not to, I think PastroLikelihood._get_selection_factor should use the same definition, it'll make the code a bit neater.

I would also rather the default be fiducial_selection=1, rather than the current 0.005. This is also an arbitrary number, but less confusing to see hard-coded in. Finally on this argument, can you remove the log message from the HyperparameterLikelihood, although I think it should be a warning in the PastroLikelihood. In the same vein, maybe we should add a warning if self.data['prior'] is 1 everywhere for the new likelihood.

Also, please remove all reference to pastro from the main likelihood class. This will require adding an __init__ method to the new likelihood class.

Sorry for the long comment...

[shanikagalaudage]

@ColmTalbot thanks! I will implement these changes.

Similarly, unless there's a reason not to, I think PastroLikelihood._get_selection_factor should use the same definition, it'll make the code a bit neater.

There is a difference being the _get_selection_factor for the general likelihood is multiplied by the number of posteriors and PastroLikelihood._get_selection_factor. Changing the function to be more general and omit the number of posteriors would make the code cleaner.

This will require adding an __init__ method to the new likelihood class.

This would involve just copying and pasting what I currently have in the init function to the PastroLikelihood, correct?