论文标题
IID从后dirichlet过程混合物中抽样
IID Sampling from Posterior Dirichlet Process Mixtures
论文作者
论文摘要
Dirichlet工艺混合物的影响在贝叶斯非参数文献中无处不在。但是，尽管马尔可夫链蒙特卡洛方法出现了，但从后部分布中进行的采样仍然是一个挑战。主要的挑战是无限维度设置，即使将无限维度随机措施集成在一起，高维度和离散性仍然仍然难以解决。 在本文中，利用Bhattacharya（2021b）提出的关键思想，我们提出了一种新的方法，用于从Dirichlet过程混合物的后代绘制IID实现。我们特别关注Bhattacharya（2008）的更通用和灵活的模型，因此此处开发的方法仅适用于传统的Dirichlet工艺混合物。 我们说明了关于众所周知的酶，酸度和星系数据集的想法，这些酶，通常被视为用于混合应用的基准数据集。在我们的并行实现中，从Bhattacharya（2008）的Dirichlet过程混合物后部产生了10,000 IID实现的实现。
The influence of Dirichlet process mixture is ubiquitous in the Bayesian nonparametrics literature. But sampling from its posterior distribution remains a challenge, despite the advent of various Markov chain Monte Carlo methods. The primary challenge is the infinite-dimensional setup, and even if the infinite-dimensional random measure is integrated out, high-dimensionality and discreteness still remain difficult issues to deal with. In this article, exploiting the key ideas proposed in Bhattacharya (2021b), we propose a novel methodology for drawing iid realizations from posteriors of Dirichlet process mixtures. We focus in particular on the more general and flexible model of Bhattacharya (2008), so that the methods developed here are simply applicable to the traditional Dirichlet process mixture. We illustrate our ideas on the well-known enzyme, acidity and the galaxy datasets, which are usually considered benchmark datasets for mixture applications. Generating 10, 000 iid realizations from the Dirichlet process mixture posterior of Bhattacharya (2008) given these datasets took 19 minutes, 8 minutes and 5 minutes, respectively, in our parallel implementation.
