Metropolis-Hastings algorithm

MCMC methods
• Markov chain Monte Carlo methods:
– Class of algorithms for sampling from a probability distribution.
– Based on constructing a Markov chain.
– Desired distribution is the equilibrium distribution.
• State of Markov chain after many steps then used as a sample of
the desired distribution.
– Quality of the sample improves as the number of steps increases.
• Difficult problem is to determine how many steps are needed to
converge to the stationary distribution within an acceptable
error.
– A good algorithm will have rapid mixing: the stationary
distribution is reached quickly starting from an arbitrary position.
– Metropolis-Hastings algorithm has rapid-mixing gproperties.
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