We propose a multistage method for making inference at all levels of a Bayesian hierarchical model (BHM) using natural data partitions to increase efficiency by allowing computations to take place in parallel form using software that is most appropriate for each data partition. The full hierarchical model is then approximated by the product of independent normal distributions for the data component of the model. In the second stage, the Bayesian maximum a posteriori (MAP) estimator is found by maximizing the approximated posterior density with respect to the parameters. If the parameters of the model can be represented as normally distributed random effects, then the second-stage optimization is equivalent to fitting a multivariate normal linear mixed model. We consider a third stage that updates the estimates of distinct parameters for each data partition based on the results of the second stage. The method is demonstrated with two ecological data sets and models, a generalized linear mixed effects model (GLMM) and an integrated population model (IPM). The multistage results were compared to estimates from models fit in single stages to the entire data set. In both cases, multistage results were very similar to a full MCMC analysis. Supplementary materials accompanying this paper appear online.

我们提出了一种多阶段方法，用于使用自然数据分区在贝叶斯层次模型 (BHM) 的所有级别上进行推理，通过允许使用最适合每个数据分区的软件以并行形式进行计算，从而提高效率。然后通过模型数据组件的独立正态分布的乘积来近似完整的层次模型。第二阶段，贝叶斯最大后验(MAP) 估计器是通过最大化关于参数的近似后验密度来找到的。如果模型的参数可以表示为正态分布的随机效应，那么第二阶段优化就相当于拟合一个多元正态线性混合模型。我们考虑第三阶段，它根据第二阶段的结果更新每个数据分区的不同参数的估计。该方法通过两个生态数据集和模型进行了演示，即广义线性混合效应模型 (GLMM) 和综合种群模型 (IPM)。将多阶段结果与模型的估计值进行比较，这些模型适合单个阶段到整个数据集。在这两种情况下，多阶段结果与完整的 MCMC 分析非常相似。本文随附的补充材料出现在网上。