Dirichlet process and Bayesian nonparametricmodels
Junxi Zhang, Yaozhong Hu · Scientia Sinica Mathematica · 2021
Bayesian nonparametric models have been extensively developed and widely used in statistics, machine learning and other areas since the ground breaking work of Ferguson. The fundamental of Bayesian nonparametric models is a special class of random probability measures: Dirichlet processes. This paper introduces the constructions, properties and some recent developments of the Dirichlet processes as well as their applications to Bayesian nonparametric estimation problems. We are also concerned with two-parameter Poisson-Dirichlet processes, Beta processes and more general stick-breaking processes and their properties.