Before revision:  The proposed VB method is benchmarked against MCMC in a simulation study. The results suggest that VB is substantially faster than MCMC but also noticeably less accurate, because the mean-field assumption of VB is too restrictive. Future research should thus focus on enhancing the expressiveness and flexibility of the variational approximation .
After revision:  The proposed VB method against MSL and MCMC in terms of parameter recovery, predictive accuracy and computational efficiency. The simulation study demonstrates that VB can be a fast and scalable alternative to MSL and MCMC, especially in applications in which fast predictions are paramount, as VB is observed to be between 2.8 and 17.7 times faster than the two competing methods. Furthermore, the simulation study shows that a parallelised implementation of the MSL estimator with analytical gradients is a viable alternative to MCMC in terms of both estimation accuracy and computational efficiency. In the considered experimental settings, the MSL estimator is between 0.9 and 2.1 times faster than MCMC .