This abstract concerns the expressive power of probabilistic programming as a method for building statistical models that are \emph{non-parametric}: the parameter space is of unbounded dimension, allowing for model exploration. Recent progress provides expressive nonparametric programming with models such as jump processes and the Dirichlet process. The Indian Buffet Process presents one frontier in expressivity, and this is our focus.

The Indian Buffet Process (IBP) is a statistical model for feature assignment. It is nonparametric in that the number of features is unbounded. Previous approaches to expressing IBP had gone outside the pure probabilistic programming paradigm by introducing hidden state or by truncating the model. We make progress by introducing a slice sampling method, and show that with \emph{nested inference} we can express the IBP fully.