  This paper discusses the efficient Bayesian estimation of a multivariate
factor stochastic volatility (Factor MSV) model with leverage. We propose a
novel approach to construct the sampling schemes that converges to the
posterior distribution of the latent volatilities and the parameters of
interest of the Factor MSV model based on recent advances in Particle Markov
chain Monte Carlo (PMCMC). As opposed to the approach of Chib et al. (2006} and
Omori et al. (2007}, our approach does not require approximating the joint
distribution of outcome and volatility innovations by a mixture of bivariate
normal distributions. To sample the free elements of the loading matrix we
employ the interweaving method used in Kastner et al. (2017} in the Particle
Metropolis within Gibbs (PMwG) step. The proposed method is illustrated
empirically using a simulated dataset and a sample of daily US stock returns.
