Combining chains of Bayesian models with Markov melding

Abstract

A challenge for practitioners of Bayesian inference is specifying a model that incorporates multiple relevant, heterogeneous data sets. It may be easier to instead specify distinct submodels for each source of data, then join the submodels together. We consider chains of submodels, where submodels directly relate to their neighbours via common quantities which may be parameters or deterministic functions thereof. We propose chained Markov melding, an extension of Markov melding, a generic method to combine chains of submodels into a joint model. One challenge we address is appropriately capturing the prior dependence between common quantities within a submodel, whilst also reconciling differences in priors for the same common quantity between two adjacent submodels. Estimating the posterior of the resulting overall joint model is also challenging, so we describe a sampler that uses the chain structure to incorporate information contained in the submodels in multiple stages, possibly in parallel. We demonstrate our methodology using two examples. The first example considers an ecological integrated population model, where multiple data sets are required to accurately estimate population immigration and reproduction rates. We also consider a joint longitudinal and time-to-event model with uncertain, submodel-derived event times. Chained Markov melding is a conceptually appealing approach to integrating submodels in these settings.

arXiv comment37 pages, 14 figures. Revisions to text

References in corpus (15)

• Rank-normalization, folding, and localization: An improved $\hat{R}$ for assessing convergence of MCMC
• Visualization in Bayesian workflow
• Programming with models: writing statistical algorithms for general model structures with NIMBLE
• Joint Models with Multiple Longitudinal Outcomes and a Time-to-Event Outcome: a Corrected Two-Stage Approach
• Bayesian Survival Analysis Using the rstanarm R Package
• Divide-and-Conquer with Sequential Monte Carlo
• Joining and splitting models with Markov melding
• Combining probability distributions: Extending the logarithmic pooling approach
• Reuse, recycle, reweigh: Combating influenza through efficient sequential Bayesian computation for massive data
• Synthesising evidence to estimate pandemic (2009) A/H1N1 influenza severity in 2009-2011
• A Bayesian Hierarchical Network for Combining Heterogeneous Data Sources in Medical Diagnoses
• A numerically stable algorithm for integrating Bayesian models using Markov melding
• The divide-and-conquer sequential Monte Carlo algorithm: theoretical properties and limit theorems
• Combining chains of Bayesian models with Markov melding
• A Bayesian hierarchical modeling approach to combining multiple data sources: A case study in size estimation

Cited by in corpus (1)

• Combining chains of Bayesian models with Markov melding