# Thread: Markov chain monte carlo

1. ## Markov chain monte carlo

who knows the answer to this multiple choice question?

Regarding Markov Chain Monte Carlo (MCMC) techniques, it is incorrect to state that:
a) an ergodic Markov chain can have multiple equilibrium distributions.
b) if the Markov chain satisfies detailed balance, the required distribution will be invariant to it,
c) if the Markov chain is reversible, the required distribution will be invariant to it,
d) MCMC simulates a Markov chain such that states from the Markov chain converge to some desired probability distribution.

thanks

2. I'm assuming ergodic means irreducible, positive recurrent and aperiodic. In which case, a) is incorrect because an ergodic Markov chain has a unique equilibrium distribution.

b) is correct
c) satisfying detailed balance is equivalent to reversible.
d) That's the purpose of MCMC