Flexible Variational Bayes based on a Copula of a Mixture

Understand

Variational Bayes methods approximate the posterior density by a family of tractable distributions whose parameters are estimated by optimisation.

• 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.