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## Abstract

This work describes the possibilities and limits of Probabilistic Programming, which is a new approach to statistical modelling using programming languages to describe arbitrary complex statistical models. Probabilistic Programming Systems aim to introduce an abstraction layer over inference algorithms making them easier to use by hiding the complexity of statistical inference from the user.

This work gives a small background on the statistical concepts used in Probabilistic Programming and describes the state of the art of inference algorithms that can be used to build inference engines that can work on all possible statistical models. It also gives a short overview over the computability of probability distributions which describes the upper limit of what is possible with the Probabilistic Programming approach.