Implement grad for GammaInc

[MrinankSharma]

The Gamma logcdf does not have a gradient function implemented.

Example:

self.GI_mean = pm.Normal('GI_mean', gi_mean_mean, gi_mean_sd)
self.GI_sd = pm.Normal('GI_sd', gi_sd_mean, gi_sd_sd)

gi_beta = self.GI_mean / self.GI_sd ** 2
gi_alpha = self.GI_mean ** 2 / self.GI_sd ** 2

GI_dist = pm.Gamma.dist(alpha=gi_alpha, beta=gi_beta)

bins = np.zeros(gi_truncation + 1)
bins[1:] = np.arange(gi_truncation)
bins[2:] += 0.5
bins[:2] += 1e-5

cdf_vals = T.exp(GI_dist.logcdf(bins))
pmf = cdf_vals[1:] - cdf_vals[:-1]
GI_rev = T.repeat(T.reshape(pmf[::-1] / T.sum(pmf), (1, 1, gi_truncation)), 2, axis=0)

Trying to sample from this raises an error:

MethodNotDefined: ('grad', <class 'theano.scalar.basic_scipy.GammaInc'>, 'GammaInc')

Note: the logcdf derivative should be available as a function of the logpdf. It would be great to have this implemented. For example, this would mean my use case above (generating a discretised distribution) can be implemented.

[twiecki]

Thanks for reporting -- want to do a PR?

[MrinankSharma]

Thanks for reporting -- want to do a PR?

I'd be up for working on a PR, but I've never submitted a PR on the PyMC3 codebase before. If you think this can be tackled by a newcomer, I can give it a go.

[twiecki]

I think you'd learn a lot and we'll definitely help out.