A numerically stable algorithm for integrating Bayesian models using Markov melding
Publication Date
2022-04-15Journal Title
Statistics and Computing
ISSN
0960-3174
Publisher
Springer Science and Business Media LLC
Volume
32
Issue
2
Language
en
Type
Article
This Version
VoR
Metadata
Show full item recordCitation
Manderson, A., & Goudie, R. (2022). A numerically stable algorithm for integrating Bayesian models using Markov melding. Statistics and Computing, 32 (2) https://doi.org/10.1007/s11222-022-10086-2
Abstract
<jats:title>Abstract</jats:title><jats:p>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.</jats:p>
Keywords
Article, Biased sampling, Data integration, Evidence synthesis, Kernel density estimation, Multi-source inference, Self-density ratio, Weighted sampling
Sponsorship
MRC (unknown)
Alan Turing Institute (Andrew Manderson)
Identifiers
s11222-022-10086-2, 10086
External DOI: https://doi.org/10.1007/s11222-022-10086-2
This record's URL: https://www.repository.cam.ac.uk/handle/1810/335090
Rights
Licence:
http://creativecommons.org/licenses/by/4.0/
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