Abstract

Our object of study is the general class of stick-breaking processes with exchangeable length variables. These generalize well-known Bayesian nonparametric priors in an unexplored direction. We give conditions to assure the respective species sampling process is proper and the corresponding prior has full support. For a rich subclass we explain how, by tuning a single $[0,1]$-valued parameter, the stochastic ordering of the weights can be modulated, and Dirichlet and Geometric priors can be recovered. A general formula for the distribution of the latent allocation variables is derived and an MCMC algorithm is proposed for density estimation purposes.

摘要

我们的研究对象是具有可交换长度变量的一般类断棒过程。这些在未探索的方向上推广了众所周知的贝叶斯非参数先验。我们提供条件以确保各个物种的采样过程是适当的，并且相应的先验得到充分支持。对于丰富的子类，我们解释了如何通过调整单个 $[0,\mathrm{1个}]$值参数，可以调制权重的随机排序，并且可以恢复 Dirichlet 和几何先验。推导了潜在分配变量分布的一般公式，并提出了用于密度估计目的的 MCMC 算法。