Consider the following acceptance probability for the Metropolis Hastings algorithm (x, y) (y) (x) (y) Show that this definition of (x, y) produces a reversible Markov chain and has the stationary distribution if the transition probability q(x y) is symmetric

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Question: Consider the following acceptance probability for the Metropolis-Hastings algorithm: (x, y) = (y) (x) + (y) Show that this definition of (x, y) produces a

Consider the following acceptance probability for the Metropolis-Hastings algorithm:

α(x, y) = π(y)

π(x) + π(y)

Show that this definition of α(x, y) produces a reversible Markov chain and has the stationary distribution π if the transition probability q(x|y) is symmetric.

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