Recall MH sampling for target distribution p(x) using proposal q(x|y): at states, first draw t ~...

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Recall MH sampling for target distribution p(x) using proposal q(x|y): at states, first draw t ~ q(t|s), then accept t with probability A = min (1. p(t)q(s|t) p(s)q(t|s) where p(x) is the unnormalized target distribution. Show that p(x) is the stationary distribution of the Markov chain defined by this procedure. Consider both continuous and discrete cases. Recall MH sampling for target distribution p(x) using proposal q(x|y): at states, first draw t ~ q(t|s), then accept t with probability A = min (1. p(t)q(s|t) p(s)q(t|s) where p(x) is the unnormalized target distribution. Show that p(x) is the stationary distribution of the Markov chain defined by this procedure. Consider both continuous and discrete cases.