Add hyper-parameter likelihood

See #69 (closed)

mentioned in issue #69 (closed)

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• c5b4e903 - Rewrite hyperparameter likelihood with logged priors

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• cef702bd - Add an example showing how to use the hyper parameter likelihood

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This is a nice start. Can I recommend that we use the DataFrame from the initial inference, this will make it much easier to handle arbitrary posteriors and keep track of large numbers of parameters in the likelihood. It may seem like overkill in the very simple case here but having

hyper_prior = np.exp(- (posterior['mu'] - mu_m)**2 / (2 * sigma_m)) / (2 * np.pi * sigma_m**2)**0.5

will make it much simpler going forward.

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• 452f593b - Assume the inputs are tupak Prior classes

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changed title from WIP: Add initial version to WIP: Add hyper-parameter likelihood

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• cb1b11af - Update example to work with changes in the HierarchicalLikelihood
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• 3d671cad - Fix log prior for PowerLaw
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unmarked as a Work In Progress

This is now working and ready to be merged. It uses tupak priors rather than getting the user to write them out themselves. This is advantageous for most cases where we will use a well defined prior, but adds a little complexity if you want to do something non-standard (you have to define a Prior).

@colm.talbot , I like your idea to use the posterior, but we don't really need that now that it uses the Prior

There are thing that are a little ugly

1. We are forced to use the parameter names defined in the standard Prior classes (i.e. mu and sigma for a normal distribution). You can circumvent this by writing your own Prior class though.

2. You have to pass the parameters into the likelihood in order to figure out which parameters to sample over (i.e mu=None, sigma=None). It's good as it is explicit, but notationwise looks a bit weird.

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assigned to @colm.talbot

It uses tupak priors rather than getting the user to write them out themselves. This is advantageous for most cases where we will use a well defined prior, but adds a little complexity if you want to do something non-standard (you have to define a Prior).

This is nice, I like that it makes that it's a prior ratio super explicit. It may require a little more sophistication in the interpolated priors, something with properties maybe, I'll have a think. I'm personally happy with building new Prior classes, it's similar to what I've been doing.

I like your idea to use the posterior, but we don't really need that now that it uses the Prior

I'm not sure these are related. The posterior would take the place of samples, although I guess there's nothing to stop individual users from doing this on their.

You have to pass the parameters into the likelihood in order to figure out which parameters to sample over (i.e mu=None, sigma=None). It's good as it is explicit, but notationwise looks a bit weird.

Can we not just pass a list of parameter names? Actually, this would probably work with a Priors class. Then you just check which names appear in both the new prior and the old prior and use that as your keys.

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• 20f0eb40 - Remove parameters argument from HLikelihood and set from hyper_prior

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