API change maxent and quartile functions

[aloctavodia]

maxent and quartile both accept a distribution, modify it in place and by default plot the modified distribution. They both return the axes and the optimization object from scipy.optimize. This is usually ok. But there are instances that a different behaviour will be more useful for instance a common pattern when working with GPs in PyMC is to do something like this

ell_t_params = pm.find_constrained_prior(
    pm.Lognormal, lower=0.5, upper=4.0, mass=0.95, init_guess={"mu": 1.0, "sigma": 1.0}
)
ell_t = pm.Lognormal("ell_t", **ell_t_params)

To do that with maxent we need to write something like

dist = pz.Lognormal()
pz.maxent(dist, 0.5, 4, 0.95, plot=False)
ell_t = pm.Lognormal("ell_t", **zip(dist.param_names, dist.params)

Those extra steps are annoying. We should have something that allows a single line, like this:

ell_t_params = pz.maxent(pz.Lognormal(), 0.5, 4, 0.95, return_params=True)
ell_t = pm.Lognormal("ell_t", **ell_t_params)

This will disable the plot and change the output from (axes, opt-object) to dict

What do you think? What other alternatives could we implement?

[aloctavodia]

This is related to #518

[aloctavodia]

Maybe something even simpler is to get rid of the optimization object, it will not be useful for most users anyway (or we can save it as an attribute) and instead return a tuple with the two elements, first the axes and second the dict with names:vals. So we should be able to do this

_, ell_t_params = pz.maxent(pz.Lognormal(), 0.5, 4, 0.95, plot=False)
ell_t = pm.Lognormal("ell_t", **ell_t_params)

[bwengals]

My least favorite thing about

ell_t_params = pm.find_constrained_prior(
    pm.Lognormal, lower=0.5, upper=4.0, mass=0.95, init_guess={"mu": 1.0, "sigma": 1.0}
)
ell_t = pm.Lognormal("ell_t", **ell_t_params)

is having to write pm.Lognormal twice.

Would it be crazy to do something like

ell_t = pz.maxent(pz.Lognormal, 0.5, 4, 0.95, pymc_kwargs={"name": "ell_t"})

or similar, and make it a one liner somehow?

[bwengals]

I do also like what you had here

_, ell_t_params = pz.maxent(pz.Lognormal(), 0.5, 4, 0.95, plot=False)
ell_t = pm.Lognormal("ell_t", **ell_t_params)

[aloctavodia]

Thanks for the input! This makes me think that we need a .to_pymc() method so we can do

ell_t = pz.maxent(pz.LogNormal(), 0.5, 4, 0.95, plot=False).to_pymc("ell_t")