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Article: A history of the Metropolis-Hastings algorithm.
- Article from:
- The American Statistician
- Article date:
- November 1, 2003
- Author:
CopyrightCOPYRIGHT 2003 American Statistical Association. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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1. INTRODUCTION
The Metropolis-Hastings (M-H) algorithm, a Markov chain Monte Carlo (MCMC) method, is one of the most popular techniques used by statisticians today. It is primarily used as a way to simulate observations from unwieldy distributions. The algorithm produces a Markov chain whose members' limiting distribution is the target density [pi]([chi]). At step j, an observation [[chi].sub.j] is generated from an instrumental density q(.|[[chi].sub.i]) (which is typically easy to simulate from). This candidate observation becomes the next value in the Markov chain with probability
[rho] = min { [pi]([[chi].sub.j])q([[chi].sub.i]|[[chi].sub.j])/ [pi] ...