Metropolis-Hastings sampling

Metropolis–Hastings algorithm gets around this problem by simulating values from an arbitrary transition distribution which is simple to sample from, such as the normal distribution or the uniform distribution

The algorithm was named after the leading American physicist and computer pioneer Nicholas Constantine Metropolis (1915–1999) and the Canadian statistician W. Keith Hastings (1930–). Metropolis was the first author (with four others) of a paper in the Journal of Chemical Physics in 1953 which first conceived the algorithm for a special case in statistical physics, while Hastings extended the method to the more general case in a 1970 paper in the statistical journal Biometrika. The method then had a long gestation period so far as statisticians are concerned, not being born as a practical tool for Bayesian statistics until the 1990s (and the advent of sufficiently fast computers).


 * proposal distribution:
 * candidate value:


 * proposal density: