A numerically stable algorithm for integrating Bayesian models using Markov melding
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Journal Title
Statistics and Computing
ISSN
0960-3174
Publisher
Springer
Type
Article
This Version
AM
Metadata
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Manderson, A., & Goudie, R. A numerically stable algorithm for integrating Bayesian models using Markov melding. Statistics and Computing https://doi.org/10.17863/CAM.80953
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.
Sponsorship
MRC (unknown)
Alan Turing Institute (Andrew Manderson)
Embargo Lift Date
2025-02-01
Identifiers
This record's DOI: https://doi.org/10.17863/CAM.80953
This record's URL: https://www.repository.cam.ac.uk/handle/1810/333533
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