Critique for MCMC

Hi Ricky, I really found your page very informative and mathematical. I like how you’ve given us a machine learning prespective to MCMC. I understand that this is a very technical topic and you’ve given us a strong mathematical reasoning, but I would’ve probably given some more intuitive insight into why we need to use MCMC and how it fits into the AI big picture and gone a little easy on the mathematics to cater for people from all fields. Also how does MCMC sampling methods compare with sampling methods which have known bounds. How many samples does MCMC need to reach those bounds? Thank you for sharing this with us! Warm regards, Ritika