Hello,

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 ?