A numerically stable algorithm for integrating Bayesian models using Markov melding

Abstract

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.

arXiv comment16 pages, 5 figures, 1 table. Major revisions, with substantial changes to Section 3

References in corpus (12)

• The pseudo-marginal approach for efficient Monte Carlo computations
• Fighting Sample Degeneracy and Impoverishment in Particle Filters: A Review of Intelligent Approaches
• On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods
• Nonparametric Density Estimation for High-Dimensional Data - Algorithms and Applications
• Joint Models with Multiple Longitudinal Outcomes and a Time-to-Event Outcome: a Corrected Two-Stage Approach
• Umbrella sampling: a powerful method to sample tails of distributions
• Joining and splitting models with Markov melding
• Reuse, recycle, reweigh: Combating influenza through efficient sequential Bayesian computation for massive data
• Exploratory data analysis for moderate extreme values using non-parametric kernel methods
• Estimation of HIV Burden through Bayesian Evidence Synthesis
• Synthesising evidence to estimate pandemic (2009) A/H1N1 influenza severity in 2009-2011
• Greater Than the Sum of its Parts: Computationally Flexible Bayesian Hierarchical Modeling

Cited by in corpus (2)

• Asymptotics of cut distributions and robust modular inference using Posterior Bootstrap
• Combining chains of Bayesian models with Markov melding