论文标题
功能性的中心限制定理用于破坏杆的先验
Functional central limit theorems for stick-breaking priors
论文作者
论文摘要
我们获得了大量，经验性Glivenko-cantelli定理，中心限制定理，功能性中心极限定理的经验性强，用于各种非参数贝叶斯先验的实用性定理，其中包括带有一般粘性重量的迪里奇过程，Poisson-dirichlet过程，正常的豪斯流程，正常化的gussian forversized forsized dirich dirich dirich dirich dirich dirich dirich，以及普遍化的dirich，以及普遍化的过程。对于带有一般杆重量的Dirichlet过程，我们引入了两个一般条件，以使中心极限定理和功能性中心极限定理保持。除了广义的dirichlet过程外，由于这些过程的有限维分布要么很难获得，要么很难使用，即使它们可用，我们也会使用时刻的方法来获得收敛结果。对于广义的Dirichlet过程，我们使用其有限的尺寸边缘分布来获得渐近学，尽管计算技术高度技术。
We obtain the empirical strong law of large numbers, empirical Glivenko-Cantelli theorem, central limit theorem, functional central limit theorem for various nonparametric Bayesian priors which include the Dirichlet process with general stick-breaking weights, the Poisson-Dirichlet process, the normalized inverse Gaussian process, the normalized generalized gamma process, and the generalized Dirichlet process. For the Dirichlet process with general stick-breaking weights, we introduce two general conditions such that the central limit theorem and functional central limit theorem hold. Except in the case of the generalized Dirichlet process, since the finite dimensional distributions of these processes are either hard to obtain or are complicated to use even they are available, we use the method of moments to obtain the convergence results. For the generalized Dirichlet process we use its finite dimensional marginal distributions to obtain the asymptotics although the computations are highly technical.
