Bayesian methods are the best for people who want to turn de-biasing into re-biasing, particularly when you're dealing with lots of output variables. (Generally when the variables are few, as they are in the things this document talks about, a screwy prior sticks out like a sore thumb.)

Sometimes the distribution that you ~can~ sample isn't really the distribution that you wish you could sample, and sometimes changing the prior in such a model is a way to make it behave as if it was sampled correctly to begin with.