What are best and / or standard practices for MCMC early stopping?
I have an algorithm which I want to compare with existing non-MCMC algorithms for accuracy and speed. When assessing the speed it's a bit tricky, since the speed is a function of the number of iterations I use in the Markov chain, and currently highly subjective.
I'd like some kind of more objective way of deciding when to cut the chain; ideally some sort of 'best practice' that's applicable for reasonably well behaved Markov chains.
Note that this is not some crazy algorithm that's going to jump between different apparently stable distributions every 2 weeks. It just goes up and down a bit, and then is stationary.