Nonreversible Monte Carlo. (a) Show that Markov chains with TPMs are both reversible and ergodic chains, but their product P1 P2 represents a nonreversible ergodic Monte Carlo. (b) Prove that a Markov chain with TPM P1 P2 converges faster than a chain with TPM P1 or P2.

Nonreversible Monte Carlo.

(a) Show that Markov chains with TPMs

are both reversible and ergodic chains, but their product P1 P2 represents a nonreversible ergodic Monte Carlo.

(b) Prove that a Markov chain with TPM P1 P2 converges faster than a chain with TPM P1 or P2.


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