Specifying a full Bayesian model that integrates multiple data sources can be challenging. One natural approach is to specify each individual model separately and join them afterwards. This is the approach adopted in Markov melding. However, when adjacent submodels share common quantities, as in chained Markov melding, posterior inference can be challenging for existing MCMC-based approaches. In this paper, we propose a new multi-stage sampler for chained Markov models involving an arbitrary number of submodels. The proposed sampler adopts a divide-and-conquer sequential Monte Carlo approach for the tree-structured model that fits naturally with the structure of chained Markov melding. The resulting multi-stage sampler provides a flexible alternative for sampling from complex joint models, as its separate sampling scheme for different submodels avoids the need for directly sampling from the full model. We demonstrate applications of the sampler through two examples. The first is a toy example involving 11 submodels of various types. The second example considers an ecologically integrated population model that combines multiple datasets to estimate immigration and reproduction rates.

翻译：指定一个整合多个数据源的完整贝叶斯模型可能具有挑战性。一种自然的方法是分别指定每个单独模型，随后再将它们合并，这正是马尔可夫融合所采用的方法。然而，当相邻子模型共享共同量（如在链式马尔可夫融合中）时，现有基于MCMC的方法进行后验推断可能面临困难。本文针对涉及任意数量子模型的链式马尔可夫模型，提出一种新的多阶段采样器。该采样器采用分解与征服的顺序蒙特卡洛方法处理树状结构模型，与链式马尔可夫融合的结构自然契合。所得多阶段采样器为复杂联合模型的采样提供了灵活替代方案，因其对各子模型采用独立采样方案，避免了直接从完整模型采样的需求。我们通过两个示例展示该采样器的应用：第一个是涉及11个不同类型子模型的玩具示例，第二个则考虑整合多个数据集以估计迁入率和繁殖率的生态综合种群模型。