This question is about the number of MCMC samples T required to reach a desired accuracy.
Suppose the mixing time of the Markov Chain is ,
ie the number of samples required so that for any further t, where P is Markov Chain and is the target.
Suppose that M further samples are required from P to reach the desired accuracy (due to the fact that we sample from P instead of ).
Then the overall time complexity (ie, number of samples required) is
I don't understand the last part. Shouldn't it be ?