Flexible Variational Bayes Based on a Copula of a Mixture
Journal of Computational and Graphical Statistics
Variational Bayes methods approximate the posterior density by a family of tractable distributions whose parameters are estimated by optimization. Variational approximation is useful when exact inference is intractable or very costly. Our article develops a flexible variational approximation based on a copula of a mixture, which is implemented by combining boosting, natural gradient, and a variance reduction method. The efficacy of the approach is illustrated by using simulated and real datasets to approximate multimodal, skewed and heavy-tailed posterior distributions, including an application to Bayesian deep feedforward neural network regression models. Supplementary materials, including appendices and computer code for this article, are available online.
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