"Monte Carlo" methods use random sampling to understand a system, estimate averages, or compute integrals. Monte Carlo methods were amongst the earliest applications run on electronic computers in the 1940s, and continue to see widespread use and research as our models and computational power grow. In the NIPS community, random sampling is widely used within optimization methods, and as a way to perform inference in probabilistic models. Here "inference" simply means obtaining multiple plausible settings of model parameters that could have led to the observed data. Obtaining a range of explanations tells us both what we can and cannot know from our data, and prevents us from making overconfident (wrong) predictions.

This introductory-level tutorial will describe some of the fundamental Monte Carlo algorithms, and examples of how they can be combined with models in different ways. We'll see that Monte Carlo methods are sometimes a quick and easy way to perform inference in a new model, but also what can go wrong, and some treatment of how to debug these randomized algorithms.