  Scientific analyses often rely on slow, but accurate forward models for
observable data conditioned on known model parameters. While various emulation
schemes exist to approximate these slow calculations, these approaches are only
safe if the approximations are well understood and controlled. This workshop
submission reviews and updates a previously published method, which has been
used in cosmological simulations, to (1) train an emulator while simultaneously
estimating posterior probabilities with MCMC and (2) explicitly propagate the
emulation error into errors on the posterior probabilities for model
parameters. We demonstrate how these techniques can be applied to quickly
estimate posterior distributions for parameters of the $\Lambda$CDM cosmology
model, while also gauging the robustness of the emulator approximation.
