  Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex
probability distributions. The pseudo-marginal MCMC framework only requires an
unbiased estimator of the unnormalized probability distribution function to
construct a Markov chain. However, the resulting chains are harder to tune to a
target distribution than conventional MCMC, and the types of updates available
are limited. We describe a general way to clamp and update the random numbers
used in a pseudo-marginal method's unbiased estimator. In this framework we can
use slice sampling and other adaptive methods. We obtain more robust Markov
chains, which often mix more quickly.
