The purported aim is to allow machine learning code that today requires 1000-10,000 lines of code to be written in 10-100 lines.
This works brilliantly for single shot learning. Let's say you are trying to teach a computer to recognize a handwritten character after a single example. First, you build a generative model that follows how letters are constructed: hand touches paper and makes a primitive shape (line, curve, loop, etc.). Multiple such primitives are strung together to form a character. For each example characters, infer the most likely sequence of such primitives. When a new classification is requested, take samples from the generative model for each known character. Calculate the difference in pixel value, and do this hundreds of thousands of times. You can now construct an accurate marginal probability for each known character while only needing a single example.
Powerful stuff!
[1] efficiency not guaranteed..(yet)
Edit: Here's a few curated resources: http://webppl.org/ http://www.robots.ox.ac.uk/~fwood/anglican/ http://mc-stan.org/ http://dippl.org/ https://probmods.org/