Mean field variational Bayes for elaborate distributions

International Society for Bayesian Analysis
Publication Type:
Journal Article
Bayesian Analysis, 2011, 6 (4), pp. 847 - 900
Issue Date:
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We develop strategies for mean eld variational Bayes approximate inference for Bayesian hierarchical models containing elaborate distributions. We loosely dene 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 Ex- treme Value distributions. Such models suer from the diculty that the param- eter 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) nite mixture approximations of troublesome den- sity functions. An accuracy assessment is conducted and the new methodology is illustrated in an application
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