A survey of non-exchangeable priors for Bayesian nonparametric models

There has recently been a spate of papers in the statistics and machine learning literature developing dependent stochastic processes and using them as priors in Bayesian nonparametric models. In this paper, we aim to provide a representative snapshot of the currently available models, to elucidate links between these models, and to provide an orienting view of the modern constructions of these processes. Traditional nonparametric priors such as the Dirichlet process [DP, 2], Chinese restaurant process [CRP, 3], Pitman-Yor process [4] and the Indian buffet process [IBP, 5] assume that our observations are exchangeable. Under the assumption of exchangeability the order of the data points does not change the probability distribution. Exchangeability is not a valid assumption for all data.