Variational message passing for skew t regression

Abstract

We extend recent work concerning variational approximations via message passing to accommodate approximate fitting and inference for skew t regression models. Derivation of variational message passing is challenging owing to the presence of non‐standard exponential families and numerical integration being needed. Nevertheless, the factor graph fragment approach means that algorithm updates only need to be derived once for a particular response model, which can be integrated in an arbitrarily complex model. Another advantage of our work is that all skew t parameters are inferred, rather than being held fixed. Furthermore, we show that posterior dependence arising in an auxiliary variable representation of a skew t model may lead to poor performances in terms of variational message passing approximation when using simple auxiliary variable representations of the likelihood fragment and convenient factorizations of the approximating densities. © 2018 John Wiley & Sons, Ltd.