A challenge for practitioners of Bayesian inference is specifying a model that incorporates multiple relevant, heterogeneous data. It may be easier to instead specify distinct submodels for each source of data, then join the submodels together. We consider chains of submodels, where submodels directly relate to their neighbours via common quantities which may be parameters or deterministic functions thereof. We propose chained Markov melding, an extension of Markov melding, a generic method to combine chains of submodels into a joint model. One challenge we address is appropriately capturing the prior dependence between common quantities within a submodel, whilst also reconciling differences in priors for the same common quantity between two adjacent submodels. Estimating the posterior of the resulting overall joint model is also challenging, so we describe a sampler that uses the chain structure to incorporate information contained in the submodels in multiple stages, possibly in parallel. We demonstrate our methodology using two examples. The first example considers an ecological integrated population model, where multiple data are required to accurately estimate population immigration and reproduction rates. We also consider a joint longitudinal and time-to-event model with uncertain, submodel-derived event times. Chained Markov melding is a conceptually appealing approach to integrating submodels in these settings.
翻译:贝叶斯推论的实践者面临的一项挑战是说明一种包含多种相关、不同数据的模式。我们处理的一个挑战是,如何为每个数据来源指定一个不同的子模型,然后加入子模型。我们考虑子模型链,其中子模型通过共同数量与邻居直接相关,这些数量可能是其参数或决定性功能。我们建议采用链条式的Markov 焊接法,即Markov 焊接法的延伸,这是将子模型链并入一个联合模型的一种通用方法。我们处理的一个挑战是,适当捕捉一个子模型中共同数量之间先前的依赖性,同时调和两个相邻的子模型之间相同的共同数量的前期差异。对由此形成的整体联合模型的外观的外观和时间差异也具有挑战性。我们描述一个样品,利用链式结构将子模型中的信息纳入多个阶段,可能是平行的。我们用两个例子展示了我们的方法。我们的第一个例子是生态综合人口模型,其中需要多个数据来准确估计人口移民和生殖率。我们还考虑在两个相邻的子模型中采用联合的纵向和时间对时间的模型,将这些模型与不固定的模型纳入进定型模型。