Probability theory is the branch of mathematics concerned with distributions, expected values, maximum likelihoods, the description of variation. The simplest examples are coin flips, dice rolls. Other common distributions are uniform, binomial, geometric, poisson, weibull, and a menagerie of others. Applications abound, from simulations, to gaming, to physics, statistics, engineering, economics. Consider: http://mathoverflow.com

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This document is designed to be a first-year graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build these systems. It is aimed at people who have an undergraduate-level understanding of either or, ideally, both probabilistic machine learning and programming languages.