Analysing multiple evidence sources is often feasible only via a modular approach, with separate submodels specified for smaller components of the available evidence. Here we introduce a generic framework that enables fully Bayesian analysis in this setting. We propose a generic method for forming a suitable joint model when joining submodels, and a convenient computational algorithm for fitting this joint model in stages, rather than as a single, monolithic model. The approach also enables splitting of large joint models into smaller submodels, allowing inference for the original joint model to be conducted via our multi-stage algorithm. We motivate and demonstrate our approach through two examples: joining components of an evidence synthesis of A/H1N1 influenza, and splitting a large ecology model.
Bibliographical noteFunding Information:
This work was supported by the UK Medical Research Council [programme codes MC UU 00002/2, MC UU 00002/11 and MC UU 00002/1]. We are grateful to Ian White, Sylvia Richardson, Brian Tom, Michael Sweeting, Paul Kirk, Adrian Raftery, and the 2015 Armitage lecturers (Leonhard Held and Michael Höhle) for helpful discussions of this work; and to the referees and editors for insightful comments that led to an improved manuscript. We also thank colleagues at Public Health England for providing data.
© 2019 International Society for Bayesian Analysis.
- Bayesian melding
- Evidence synthesis
- Markov combination
- Model integration