I'm just working through the math in the paper right now. To me, it looks like all of the formulas could be expressed in a probabilistic PL and MCMC could be us

I'm just working through the math in the paper right now. To me, it looks like all of the formulas could be expressed in a probabilistic PL and MCMC could be used to estimate the probabilities of both latent state and parameters. Would there be some particular roadblocks to this approach?