Importance Sampling Schemes for Evidence Approximation in Mixture Models

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aut.researcherLee, Jeong
dc.contributor.authorLee, Jen_NZ
dc.contributor.authorRobert, CPen_NZ
dc.date.accessioned2019-09-05T22:38:08Z
dc.date.available2019-09-05T22:38:08Z
dc.date.copyright2014-11-13en_NZ
dc.date.issued2014-11-13en_NZ
dc.description.abstractThe marginal likelihood is a central tool for drawing Bayesian inference about the number of components in mixture models. It is often approximated since the exact form is unavailable. A bias in the approximation may be due to an incomplete exploration by a simulated Markov chain (e.g., a Gibbs sequence) of the collection of posterior modes, a phenomenon also known as lack of label switching, as all possible label permutations must be simulated by a chain in order to converge and hence overcome the bias. In an importance sampling approach, imposing label switching to the importance function results in an exponential increase of the computational cost with the number of components. In this paper, two importance sampling schemes are proposed through choices for the importance function; a MLE proposal and a Rao-Blackwellised importance function. The second scheme is called dual importance sampling. We demonstrate that this dual importance sampling is a valid estimator of the evidence and moreover show that the statistical efficiency of estimates increases. To reduce the induced high demand in computation, the original importance function is approximated but a suitable approximation can produce an estimate with the same precision and with reduced computational workload.
dc.identifier.citationarXiv:1311.6000 [stat.CO]
dc.identifier.urihttps://hdl.handle.net/10292/12796
dc.publisherarXiven_NZ
dc.relation.urihttps://arxiv.org/abs/1311.6000en_NZ
dc.rightsarXiv places no restrictions on whether articles also appear in local institutional repositories. Authors are welcome to download copies of their own articles from arXiv in order to submit to a local repository.
dc.rights.accessrightsOpenAccessen_NZ
dc.subjectModel evidence; Importance sampling; Mixture models; Marginal likelihood
dc.titleImportance Sampling Schemes for Evidence Approximation in Mixture Modelsen_NZ
pubs.elements-id328735
pubs.organisational-data/AUT
pubs.organisational-data/AUT/Design & Creative Technologies
pubs.organisational-data/AUT/Design & Creative Technologies/Engineering, Computer & Mathematical Sciences
pubs.organisational-data/AUT/PBRF
pubs.organisational-data/AUT/PBRF/PBRF Design and Creative Technologies
pubs.organisational-data/AUT/PBRF/PBRF Design and Creative Technologies/PBRF ECMS
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