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This paper discusses the efficient Bayesian estimation of a multivariatefactor stochastic volatility (Factor MSV) model with leverage. We propose anovel approach to construct the sampling schemes that converges to theposterior distribution of the latent volatilities and the parameters ofinterest of the Factor MSV model based on recent advances in Particle Markovchain Monte Carlo (PMCMC). As opposed to the approach of Chib et al. (2006} andOmori et al. (2007}, our approach does not require approximating the jointdistribution of outcome and volatility innovations by a mixture of bivariatenormal distributions. To sample the free elements of the loading matrix weemploy the interweaving method used in Kastner et al. (2017} in the ParticleMetropolis within Gibbs (PMwG) step. The proposed method is illustratedempirically using a simulated dataset and a sample of daily US stock returns.

Efficient Bayesian inference for multivariate factor stochastic volatility models with leverage