Variational Bayesian methods can sometimes be a good alternative to Markov Chain Monte Carlo numerical evaluation of probability distributions. They do this, as I understand it, by approximating the priors and posteriors as products of distributions for each parameter (mean field approximation). If prior and posterior distributions are conjugate (as is the case for many exponential families of distribution) then the resulting integrals are tractable, and VB methods stand a chance of working.
Would it be possible to use VB methods where some/all of my parameters are modelled by truncated distributions?
Specifically, I am interested in using truncated multivariate normal distributions, but anything with "hard limits" would be relevant. I want to know whether I could use VB methods instead of the MCMC methods I currently use for this.