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

A numerically stable algorithm for integrating Bayesian models using Markov melding