Metropolis–Hastings algorithm: Difference between revisions

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The Metropolis–Hastings algorithm involves designing a Markov process (by constructing transition probabilities) which fulfills the two above conditions, such that its stationary distribution <math>\pi(x)</math> is chosen to be <math>P(x)</math>. The derivation of the algorithm starts with the condition of detailed balance:

<math>P(x' | x)P(x) = P(x', x) = P(x | x')P(x')</math>

which is re-written as