  While Bayesian neural networks have many appealing characteristics, current
priors do not easily allow users to specify basic properties such as expected
lengthscale or amplitude variance. In this work, we introduce Poisson Process
Radial Basis Function Networks, a novel prior that is able to encode amplitude
stationarity and input-dependent lengthscale. We prove that our novel
formulation allows for a decoupled specification of these properties, and that
the estimated regression function is consistent as the number of observations
tends to infinity. We demonstrate its behavior on synthetic and real examples.
