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| In [[mathematics]] and [[physics]], the '''hybrid Monte Carlo''' algorithm, also known as '''Hamiltonian Monte Carlo''', is a [[Markov chain Monte Carlo]] method for obtaining a sequence of [[Sampling (statistics)|random samples]] from a [[probability distribution]] for which direct sampling is difficult. This sequence can be used to approximate the distribution (i.e., to generate a histogram), or to compute an [[integral]] (such as an [[expected value]]).
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| It differs from the [[Metropolis–Hastings algorithm]] by reducing the correlation between successive states sampled by using a [[Hamiltonian mechanics|Hamiltonian]] evolution between states and additionally by targeting states with a higher acceptance criteria the observed probability distribution. This causes it to converge more quickly to the absolute probability distribution. It was devised by Simon Duane, A.D. Kennedy, Brian Pendleton and Duncan Roweth in 1987.<ref>{{cite journal|last=Duane|first=Simon|coauthors=A.D. Kennedy, Brian J. Pendleton, and Duncan, Roweth|title=Hybrid Monte Carlo|journal=Physics Letters B|date=3|year=1987|month=September|volume=195|issue=2|pages=216–222|accessdate=21 June 2011|url=http://www.sciencedirect.com/science/article/pii/037026938791197X|doi=10.1016/0370-2693(87)91197-X }}</ref> It proposes a state based on an arbitrary choice function <math>P_c</math>, which dictates the probability of choosing any state <math>i</math> and then accepts or rejects the proposed state with probability
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| <center><math>\min\left(1,\frac{P_s(i)P_c(i \rightarrow j)}{P_s(j)P_c(j \rightarrow i)}\right)</math>,</center>
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| this acceptance criteria has the convenient property of maintaining [[detailed balance]] for any <math>P_c</math>.
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| == Notes ==
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| {{Reflist}}
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| == References ==
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| * {{cite book
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| |last=Neal
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| |first=Radford M
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| |title=Handbook of Markov Chain Monte Carlo
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| |year=2011
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| |publisher=Chapman and Hall/CRC
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| |isbn=0470177934
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| |editor=Steve Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng
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| |chapter=MCMC Using Hamiltonian Dynamics
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| |chapter-url=http://www.mcmchandbook.net/HandbookChapter5.pdf}}
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| [[Category:Monte Carlo methods]]
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Latest revision as of 14:48, 5 May 2014
Metallurgist Frederick from Unionville, spends time with passions including football, semenax and home brewing. Will shortly embark on a contiki voyage that will contain visiting the Tsodilo.
Feel free to surf to my blog post; buy semenax