A numerically stable algorithm for integrating Bayesian models using Markov melding

Manderson, Andrew A.; Goudie, Robert J. B.

doi:10.48550/arxiv.2001.08038

Cited by 2 publications

(2 citation statements)

References 32 publications

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“…The proposal of this article participates in an emerging range of alternatives to standard Bayesian inference, designed to retain the benefits of fully probabilistic approaches while addressing the issue of model misspecification, and specifically here the setting of models built of multiple modules [Liu et al, 2009, Jacob et al, 2017, Leonelli et al, 2018, Goudie et al, 2019, Manderson and Goudie, 2020.…”

Section: Discussionmentioning

confidence: 99%

Asymptotics of cut distributions and robust modular inference using Posterior Bootstrap

Pompe¹,

Jacob²

2021

Preprint

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Bayesian inference provides a framework to combine an arbitrary number of model components with shared parameters, allowing joint uncertainty estimation and the use of all available data sources. However, misspecification of any part of the model might propagate to all other parts and lead to unsatisfactory results. Cut distributions have been proposed as a remedy, where the information is prevented from flowing along certain directions. We consider cut distributions from an asymptotic perspective, find the equivalent of the Laplace approximation, and notice a lack of frequentist coverage for the associate credible regions. We propose algorithms based on the Posterior Bootstrap that deliver credible regions with the nominal frequentist asymptotic coverage. The algorithms involve numerical optimization programs that can be performed fully in parallel. The results and methods are illustrated in various settings, such as causal inference with propensity scores and epidemiological studies.

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Section: Discussionmentioning

confidence: 99%

Asymptotics of cut distributions and robust modular inference using Posterior Bootstrap

Pompe¹,

Jacob²

2021

Preprint

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“…Our currently sampler is also sensitive to large differences in location or scale of the target distribution between the stages. The impact of these differences can be ameliorated using Manderson and Goudie (2021), and, more generally, Sequential Monte Carlo samplers are likely to perform better in these settings.…”

Section: Discussionmentioning

confidence: 99%

Combining chains of Bayesian models with Markov melding

Manderson,

Goudie

2021

Preprint

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A challenge for practitioners of Bayesian inference is specifying a model that incorporates multiple relevant, heterogeneous data. 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 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.

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A numerically stable algorithm for integrating Bayesian models using Markov melding

Cited by 2 publications

References 32 publications

Asymptotics of cut distributions and robust modular inference using Posterior Bootstrap

Asymptotics of cut distributions and robust modular inference using Posterior Bootstrap

Combining chains of Bayesian models with Markov melding

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