论文标题
大型样本渐近分析以独立增量进行归一化随机测量
Large sample asymptotic analysis for normalized random measures with independent increments
论文作者
论文摘要
具有独立增量的归一化随机度量代表了一类贝叶斯非标准先验，并广泛用于贝叶斯非参数框架中。在本文中，我们通过相应的征税强度对归一化随机度量（NRMIS）提供了后验一致性分析，用于表征NRMIS构建中完全随机的度量。在征税强度上引入了假设，以分析NRMI的后验一致性，并通过多个有趣的例子进行了验证。本文的重点是当样本的真实分布离散或连续时，归一化广义伽马过程（NGGP）的Bernstein-Von Mises定理。当将Bernstein-Von Mises定理应用于构建可信集时，除了通常的形式外，左端点上还会在离散时与真实分布的原子的数量密切相关。我们还讨论了伯恩斯坦 - 冯·米塞斯收敛下NGGP模型参数的影响。最后，为了进一步解释在构建可信集合中添加偏差校正的必要性，我们以数值说明偏差校正如何在离散分发时通过可靠集的可靠集对真实值的覆盖范围进行说明。
Normalized random measures with independent increments represent a large class of Bayesian nonaprametric priors and are widely used in the Bayesian nonparametric framework. In this paper, we provide the posterior consistency analysis for normalized random measures with independent increments (NRMIs) through the corresponding Levy intensities used to characterize the completely random measures in the construction of NRMIs. Assumptions are introduced on the Levy intensities to analyze the posterior consistency of NRMIs and are verified with multiple interesting examples. A focus of the paper is the Bernstein-von Mises theorem for the normalized generalized gamma process (NGGP) when the true distribution of the sample is discrete or continuous. When the Bernstein-von Mises theorem is applied to construct credible sets, in addition to the usual form there will be an additional bias term on the left endpoint closely related to the number of atoms of the true distribution when it is discrete. We also discuss the affect of the estimators for the model parameters of the NGGP under the Bernstein-von Mises convergences. Finally, to further explain the necessity of adding the bias correction in constructing credible sets, we illustrate numerically how the bias correction affects the coverage of the true value by the credible sets when the true distribution is discrete.
