Convolution of distributions

[ibab]

Users should be able to incorporate convolutions of two distributions as a new distribution into the model.
This could be used to model random noise added to a random variate.

Example:

p2 = Conv(p1, Normal(0, .1))

For the implementation, we could either try to use the 2D convolution in theano or write our own using FFT.
Also, many exponential family distributions have nice analytical convolutions that we could make use of.

[cranmer]

Nice to hear from you @ibab.
There are a few different ways to implement the convolution, so we should probably have an abstraction here too.

• numerical integral for distribution
• FFT version
• known analytical pairs

Also, for the case that the distribution is just a generative model, I guess we just sample from p1 and p2 and then add per component.