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<p><b>New page</b></p><div>'''Metropolis-Hastings''' (also known as '''Metropolis-Hastings-Green''') is the main form of [[Markov chain Monte Carlo]]. The algorithm provides a probabilistic rejection rule to reject some proposed moves of an arbitrary irreducible Markov chain so that the resultant [[Markov chain]] has the desired stationary distribution.<br />
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== Properties of the chain ==<br />
* If we find a tree with a better P(D|T), we are guaranteed to add that T to the chain. <br />
* If the new tree has a worse P(D|T), we may stay with the better tree, or switch. The chance of switching depends on the relative difference.<br />
* Less likely to include trees with low P(D|T) in chain<br />
* More likely to stay with a tree with high P(D|T) for many steps.<br />
* "Climbing mountains" but allowing some chance of moving downhill as well.<br />
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== See also ==<br />
* [[Metropolis-coupled Markov chain Monte Carlo]]<br />
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[[Category:Academic Research]]<br />
[[Category:Statistics]]</div>Christoph