Paganin Sally, Herring Amy H, Olshan Andrew F, Dunson David B
Department of Environmental Science, Policy, and Management, University of California, Berkeley.
Department of Statistical Science, Duke University, Durham.
Bayesian Anal. 2021 Mar;16(1):301-370. doi: 10.1214/20-BA1197. Epub 2020 Feb 13.
There is a very rich literature proposing Bayesian approaches for clustering starting with a prior probability distribution on partitions. Most approaches assume exchangeability, leading to simple representations in terms of Exchangeable Partition Probability Functions (EPPF). Gibbs-type priors encompass a broad class of such cases, including Dirichlet and Pitman-Yor processes. Even though there have been some proposals to relax the exchangeability assumption, allowing covariate-dependence and partial exchangeability, limited consideration has been given on how to include concrete prior knowledge on the partition. For example, we are motivated by an epidemiological application, in which we wish to cluster birth defects into groups and we have prior knowledge of an initial clustering provided by experts. As a general approach for including such prior knowledge, we propose a Centered Partition (CP) process that modifies the EPPF to favor partitions close to an initial one. Some properties of the CP prior are described, a general algorithm for posterior computation is developed, and we illustrate the methodology through simulation examples and an application to the motivating epidemiology study of birth defects.
有大量丰富的文献提出了用于聚类的贝叶斯方法，这些方法从分区上的先验概率分布开始。大多数方法假定可交换性，从而在可交换分区概率函数（EPPF）方面产生简单的表示形式。吉布斯型先验涵盖了这类情况中的一大类，包括狄利克雷过程和皮特曼 - 约尔过程。尽管已经有一些提议放宽可交换性假设，允许协变量依赖性和部分可交换性，但对于如何纳入关于分区的具体先验知识的考虑却很有限。例如，我们受到一项流行病学应用的启发，在该应用中，我们希望将出生缺陷聚类成组，并且我们拥有专家提供的初始聚类的先验知识。作为纳入此类先验知识的一般方法，我们提出了一种中心分区（CP）过程，该过程修改EPPF以支持接近初始分区的分区。描述了CP先验的一些性质，开发了一种用于后验计算的通用算法，并且我们通过模拟示例以及将其应用于关于出生缺陷的激励性流行病学研究来说明该方法。
