Mean field variational bayes for elaborate distributions

Wand, MP; Ormerod, JT; Padoan, SA; Frührwirth, R

Mean field variational bayes for elaborate distributions

Wand, MP

Ormerod, JT Padoan, SA Frührwirth, R

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Publication Type:: Journal Article
Citation:: Bayesian Analysis, 2011, 6 (4), pp. 847 - 900
Issue Date:: 2011-12-01

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Field	Value	Language
dc.contributor.author	Wand, MP https://orcid.org/0000-0003-2555-896X	en_US
dc.contributor.author	Ormerod, JT	en_US
dc.contributor.author	Padoan, SA	en_US
dc.contributor.author	Frührwirth, R	en_US
dc.date.issued	2011-12-01	en_US
dc.identifier.citation	Bayesian Analysis, 2011, 6 (4), pp. 847 - 900	en_US
dc.identifier.issn	1936-0975	en_US
dc.identifier.uri	http://hdl.handle.net/10453/17931
dc.description.abstract	We develop strategies for mean field variational Bayes approximate inference for Bayesian hierarchical models containing elaborate distributions. We loosely define elaborate distributions to be those having more complicated forms compared with common distributions such as those in the Normal and Gamma families. Examples are Asymmetric Laplace, Skew Normal and Generalized Extreme Value distributions. Such models suffer from the difficulty that the parameter updates do not admit closed form solutions. We circumvent this problem through a combination of (a) specially tailored auxiliary variables, (b) univariate quadrature schemes and (c) finite mixture approximations of troublesome density functions. An accuracy assessment is conducted and the new methodology is illustrated in an application. © 2011 International Society for Bayesian Analysis.	en_US
dc.relation.ispartof	Bayesian Analysis	en_US
dc.relation.isbasedon	10.1214/11-BA631	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	Mean field variational bayes for elaborate distributions	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	6	en_US
utslib.for	0104 Statistics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	6	en_US

Abstract:

We develop strategies for mean field variational Bayes approximate inference for Bayesian hierarchical models containing elaborate distributions. We loosely define elaborate distributions to be those having more complicated forms compared with common distributions such as those in the Normal and Gamma families. Examples are Asymmetric Laplace, Skew Normal and Generalized Extreme Value distributions. Such models suffer from the difficulty that the parameter updates do not admit closed form solutions. We circumvent this problem through a combination of (a) specially tailored auxiliary variables, (b) univariate quadrature schemes and (c) finite mixture approximations of troublesome density functions. An accuracy assessment is conducted and the new methodology is illustrated in an application. © 2011 International Society for Bayesian Analysis.

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http://hdl.handle.net/10453/17931