2020/01/31 by Andrew A. Manderson, Robert J. B. Goudie
Computer Science · Mathematics · Medicine · #Algorithm #Artificial intelligence #Bayesian Methods and Mixture Models #Bayesian inference #Bayesian probability #Computer science #Inference #Influenza Virus Research Studies #Joins #Machine learning #Markov chain #Markov chain Monte Carlo #Markov model #Mathematics #Statistical Methods and Bayesian Inference #Variable-order Markov model #stat.AP #stat.CO #stat.ME
paper · pdf · doi:10.1007/s11222-022-10086-2
published as Statistics and Computing volume 32, Article number: 24 (2022) · 16 pages, 5 figures, 1 table. Major revisions, with substantial changes to Section 3
arxiv created 2021/09/23 · openalex publication_date 2022/02/18 · arxiv updated 2022/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.