Stochastic approximation cut algorithm for inference in modularized Bayesian models.
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Publication Date
2021-12-06Journal Title
Statistics and computing
ISSN
0960-3174
Volume
32
Language
eng
Type
Article
This Version
VoR
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Liu, Y., & Goudie, R. J. B. (2021). Stochastic approximation cut algorithm for inference in modularized Bayesian models.. Statistics and computing, 32 https://doi.org/10.1007/s11222-021-10070-2
Abstract
Bayesian modelling enables us to accommodate complex forms of data and make a comprehensive inference, but the effect of partial misspecification of the model is a concern. One approach in this setting is to modularize the model and prevent feedback from suspect modules, using a cut model. After observing data, this leads to the cut distribution which normally does not have a closed form. Previous studies have proposed algorithms to sample from this distribution, but these algorithms have unclear theoretical convergence properties. To address this, we propose a new algorithm called the stochastic approximation cut (SACut) algorithm as an alternative. The algorithm is divided into two parallel chains. The main chain targets an approximation to the cut distribution; the auxiliary chain is used to form an adaptive proposal distribution for the main chain. We prove convergence of the samples drawn by the proposed algorithm and present the exact limit. Although SACut is biased, since the main chain does not target the exact cut distribution, we prove this bias can be reduced geometrically by increasing a user-chosen tuning parameter. In addition, parallel computing can be easily adopted for SACut, which greatly reduces computation time.
Keywords
discretization, Stochastic Approximation Monte Carlo, Intractable Normalizing Functions, Cutting Feedback
Sponsorship
Medical Research Council (MC_UU_00002/2)
Cambridge Commonwealth, European and International Trust (Cambridge International Scholarship)
Identifiers
PMC7612314, 35125678
External DOI: https://doi.org/10.1007/s11222-021-10070-2
This record's URL: https://www.repository.cam.ac.uk/handle/1810/334930
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