In particular, Bayesian methods, based on the work of Reverend Thomas Bayes in the 1700s, describe how probabilities can be used to represent the degrees of belief of a rational agent. Bayesian methods work best when they are applied to models that are flexible enough to capture to complexity of real-world data. Recent work on non-parametric Bayesian methods provides this flexibility.

I will touch upon key developments in the field, including Gaussian processes, Dirichlet processes, and the Indian buffet process (IBP). Focusing on the IBP, I will describe how this can be used in a number of applications such as collaborative filtering, bioinformatics, cognitive modelling, independent components analysis, and causal discovery. Finally, I will outline the main challenges in the field: how to develop new models, new fast inference algorithms, and compelling applications. >