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Bayesian inference via projections

Silva, R; Kalaitzis, A; (2015) Bayesian inference via projections. Statistics and Computing , 25 (4) pp. 739-753. 10.1007/s11222-015-9557-6. Green open access

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Abstract

Bayesian inference often poses difficult computational problems. Even when off-the-shelf Markov chain Monte Carlo (MCMC) methods are available to the problem at hand, mixing issues might compromise the quality of the results. We introduce a framework for situations where the model space can be naturally divided into two components: (i) a baseline black-box probability distribution for the observed variables and (ii) constraints enforced on functionals of this probability distribution. Inference is performed by sampling from the posterior implied by the first component, and finding projections on the space defined by the second component. We discuss the implications of this separation in terms of priors, model selection, and MCMC mixing in latent variable models. Case studies include probabilistic principal component analysis, models of marginal independence, and a interpretable class of structured ordinal probit models.

Type: Article
Title: Bayesian inference via projections
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s11222-015-9557-6
Publisher version: http://dx.doi.org/10.1007/s11222-015-9557-6
Language: English
Additional information: The final publication is available at link.springer.com.
Keywords: MCMC, Optimization, Latent variable models, Structured covariance matrices
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1469572
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