## Motivating MCMC

Maybe it is my communications background, it took me long time to really “understand” why we need MCMC. Consider a really simple inference problem of trying to recover state $latex x$ from data $latex D$, in Bayesian inference, we try to compute the posterior distribution $latex p(x|D) = \frac{p(D|x) p(x)}{\int p(D|x) p(x) dx}$ In all…