The Metropolis-Hastings algorithm is a Markov chain Monte Carlo method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult. New samples are added to the sequence in two steps: a new sample is proposed based on the previous one, then it is either accepted into the sequence or rejected depending on the value of the probability distribution at that point. The resulting sequence can be used to approximate the distribution, such as to generate a histogram, or to compute an integral such as an expected value. Metropolis-Hastings and other Markov chain Monte Carlo algorithms are generally used for sampling from multi-dimensional distributions, especially when the number of dimensions is high.
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Invented By
Nicholas Metropolis led the 1953 paper introducing the Monte Carlo method later generalized by W. K. Hastings into the Metropolis-Hastings algorithm.
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