Add Gaussian Process Regressor

[alizma]

GPRs lend themselves well to the fit(), predict() methodology. Moreover, a well-done GPR will enable this package to be used for kriging, which has been used for the solution of PDEs, with an increasing interest in this topic in recent years.

[bob-carpenter]

Adding GPs would be awesome. Any ideas on how users would specify covariance functions?

P.S. "kriging" is just the name the geostats community uses for Gaussian processes. It's also closely related to the conditional autoregressive (CAR) models in spatial stats. GeoBUGS has an implementation and there are Stan case studies and a chapter in the user's guide.

P.P.S. And it's not just PDEs---people use GPs to "emulate" all sorts of models. They also use neural nets more and more for this. The relation is that a GP is like a one-hidden-layer neural network with infinite width (established in Radford Neal's 1990s Ph.D. thesis). Here's a more recent summary: https://arxiv.org/abs/1711.00165