标题： 截断随机测度 显示英文标题

标题： Truncated Random Measures

摘要： 完全随机测度（CRMs）及其归一化是贝叶斯非参数先验的一个丰富来源。 示例包括贝塔、伽马和 狄利克雷过程。 在本文中，我们详细介绍了两种主要的序列CRM表示形式——级数表示和叠加表示——在这些表示形式中，我们整理了可用于模拟和后验推断的新颖和现有的序列表示。 这两个类别及其组成部分表示涵盖了之前为特定过程以随意方式开发的现有表示。 由于无法直接使用完整的无限维CRM进行计算，通常会对序列表示进行截断以获得可处理性。 我们提供了每种序列表示类型及其归一化版本的截断误差分析，从而对文献中现有的截断误差界限进行了推广和改进。 我们分析了序列表示的计算复杂度，这与我们的误差界限相结合，使我们能够直接比较表示方法并讨论它们的相对效率。 我们包括了我们的理论结果在常用（归一化）CRMs上的许多应用，证明了我们的结果使得在贝叶斯非参数背景下以前未提供的CRM的直接表示和分析成为可能。 显示英文摘要

摘要： Completely random measures (CRMs) and their normalizations are a rich source of Bayesian nonparametric priors. Examples include the beta, gamma, and Dirichlet processes. In this paper we detail two major classes of sequential CRM representations---series representations and superposition representations---within which we organize both novel and existing sequential representations that can be used for simulation and posterior inference. These two classes and their constituent representations subsume existing ones that have previously been developed in an ad hoc manner for specific processes. Since a complete infinite-dimensional CRM cannot be used explicitly for computation, sequential representations are often truncated for tractability. We provide truncation error analyses for each type of sequential representation, as well as their normalized versions, thereby generalizing and improving upon existing truncation error bounds in the literature. We analyze the computational complexity of the sequential representations, which in conjunction with our error bounds allows us to directly compare representations and discuss their relative efficiency. We include numerous applications of our theoretical results to commonly-used (normalized) CRMs, demonstrating that our results enable a straightforward representation and analysis of CRMs that has not previously been available in a Bayesian nonparametric context.