When statistical analyses consider multiple data sources, Markov melding provides a method for combining the source-specific Bayesian models. Markov melding joins together submodels that have a common quantity. One challenge is that the prior for this quantity can be implicit, and its prior density must be estimated. We show that error in this density estimate makes the two-stage Markov chain Monte Carlo sampler employed by Markov melding unstable and unreliable. We propose a robust two-stage algorithm that estimates the required prior marginal self-density ratios using weighted samples, dramatically improving accuracy in the tails of the distribution. The stabilised version of the algorithm is pragmatic and provides reliable inference. We demonstrate our approach using an evidence synthesis for inferring HIV prevalence, and an evidence synthesis of A/H1N1 influenza.

当统计分析考虑多个数据源时，马尔可夫融合提供了一种组合源特定贝叶斯模型的方法。马尔可夫融合将具有共同数量的子模型连接在一起。一个挑战是这个量的先验可以是隐含的，并且必须估计其先验密度。我们表明，这种密度估计中的误差使马尔可夫融合所使用的两级马尔可夫链蒙特卡罗采样器不稳定且不可靠。我们提出了一种稳健的两阶段算法，该算法使用加权样本估计所需的先验边际自密度比，从而显着提高分布尾部的准确性。该算法的稳定版本是实用的，并提供可靠的推理。我们展示了我们使用证据综合来推断 HIV 流行率的方法，