A Brief Introduction to Bayesian Nonparametric Methods for Clustering and Time Series Analysis

Abstract

Many descriptions of Bayesian nonparametric methods assume advanced mathematical and statistical proficiency. The goal of this tutorial is to provide a conceptual introduction to Bayesian nonparametrics that assumes only basic knowledge of standard Bayesian statistics, while also containing a few key derivations that provide mathematical insight into the presented methods. We begin by reviewing the motivation for Bayesian nonparametric methods, including DeFinetti’s theorem. The Dirichlet process and the Chinese restaurant process (and their hier- archical counterparts) are then introduced in a clustering scenario that provides a mathematical and conceptual foundation for understanding more complex models. After reviewing the basics of Hidden Markov Models, these ideas are extended to time series analysis and augmented with priors that enable partial sharing of structure across multiple time series—the Beta process and the Indian buffet process. Finally, we close with a brief discussion of inference via Markov Chain Monte Carlo sampling methods.