We propose a Bayesian prior formulation for a multivariate GARCH model that expands the allowable parameter space, directly enforcing both necessary and sufficient conditions for positive definiteness and covariance stationarity. This extends the standard approach of enforcing unnecessary parameter restrictions. A VECH model specification is proposed allowing both parsimony and parameter interpretability, opposing existing specifications that achieve only one of these. A Markov chain Monte Carlo scheme, employing Metropolis–Hastings and delayed rejection, is designed. A simulation study shows favourable estimation and improved coverage of intervals, compared with classical methods. Finally, some US and UK financial stock returns are analysed.