混合模型的贝叶斯自助法
A Bayesian Bootstrap for Mixture Models
AI总结：
本文提出一种新的非参数贝叶斯自助法用于混合模型，通过将传统贝叶斯自助法重新解释为梯度上升算法并改用连续核，基于非参数最大似然估计工作，并证明了算法的收敛性与可交换性。
摘要：
本文通过发展传统的贝叶斯自助法，提出了一种新的用于混合模型的非参数贝叶斯自助法。我们首先将使用Pólya-urn方案的贝叶斯自助法重新解释为一种梯度上升算法，并关联了单步求解器。关键在于使用与贝叶斯自助法相同的基本机制，但将点质量核切换为连续核。正如贝叶斯自助法仅基于经验分布函数工作，新的混合模型贝叶斯自助法也仅基于混合分布的非参数最大似然估计工作。从理论角度来看，我们证明了该算法生成的样本序列的收敛性和可交换性，并通过不同的模型、设置和一些真实数据展示了我们的结果。
英文摘要：
This paper proposes a new nonparametric Bayesian bootstrap for a mixture model, by developing the traditional Bayesian bootstrap. We first reinterpret the Bayesian bootstrap, which uses the Pólya-urn scheme, as a gradient ascent algorithm which associated one-step solver. The key then is to use the same basic mechanism as the Bayesian bootstrap with the switch from a point mass kernel to a continuous kernel. Just as the Bayesian bootstrap works solely from the empirical distribution function, so the new Bayesian bootstrap for mixture models works off the nonparametric maximum likelihood estimator for the mixing distribution. From a theoretical perspective, we prove the convergence and exchangeability of the sample sequences from the algorithm and also illustrate our results with different models and settings and some real data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
