I'm not too sure about this. Isn't the usual derivation of MCMC methods based on equilibrium distribution of the chain? So you either need to run the chain for

I'm not too sure about this. Isn't the usual derivation of MCMC methods based on equilibrium distribution of the chain? So you either need to run the chain for a (unknowably) long time to achieve equilibrium (hence burn-in) or start from an equilibrium distribution - but if you knew that, you wouldn't be running MCMC. And sure, we can never tell the chain has achieved equilibrium, but that's better than calling any odd point 'equilibrium'. He does mention this stream of thought but dismisses it out of hand, without an explanation.