A numerically stable algorithm for integrating Bayesian models using Markov melding.


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Authors
Manderson, Andrew A  ORCID logo  https://orcid.org/0000-0002-4946-9016
Goudie, Robert JB 
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.

Description
Keywords
Biased sampling, Data integration, Evidence synthesis, Kernel density estimation, Multi-source inference, Self-density ratio, Weighted sampling
Journal Title
Stat Comput
Conference Name
Journal ISSN
0960-3174
1573-1375
Volume Title
32
Publisher
Springer Science and Business Media LLC
Sponsorship
MRC (unknown)
Alan Turing Institute (Andrew Manderson)