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Markov chain Monte Carlo
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=== Sources === {{refbegin|40em}} * Christophe Andrieu, Nando De Freitas, Arnaud Doucet and Michael I. Jordan [http://www.cs.princeton.edu/courses/archive/spr06/cos598C/papers/AndrieuFreitasDoucetJordan2003.pdf ''An Introduction to MCMC for Machine Learning''], 2003 * {{cite book | last1 = Asmussen | first1 = SΓΈren | last2 = Glynn | first2 = Peter W. | title = Stochastic Simulation: Algorithms and Analysis | publisher = Springer | series = Stochastic Modelling and Applied Probability | volume = 57 | year = 2007 }} *{{cite web | first = P. | last = Atzberger | url = http://web.math.ucsb.edu/~atzberg/pmwiki_intranet/uploads/AtzbergerHomePage/Atzberger_MonteCarlo.pdf | title = An Introduction to Monte-Carlo Methods }} *{{cite book | first = Bernd A. | last = Berg | author1-link = Bernd A. Berg | title = Markov Chain Monte Carlo Simulations and Their Statistical Analysis | publisher = [[World Scientific]] | year = 2004 }} *{{cite book | last = Bolstad | first = William M. | year = 2010 | title = Understanding Computational Bayesian Statistics | publisher = Wiley | isbn = 978-0-470-04609-8 }} *Carlin, Brad; Chib, Siddhartha (1995). [https://wwwf.imperial.ac.uk/~das01/MyWeb/SCBI/Papers/CarlinChib.pdf "Bayesian Model Choice via Markov Chain Monte Carlo Methods"]. ''[[Journal of the Royal Statistical Society|Journal of the Royal Statistical Society, Series B]]'', 57(3), 473–484. *{{cite journal | first1 = George | last1 = Casella | first2 = Edward I. | last2 = George | title = Explaining the Gibbs sampler | journal = [[The American Statistician]] | volume = 46 | issue = 3 | pages = 167β174 | year = 1992 | doi=10.2307/2685208 | jstor = 2685208 | citeseerx = 10.1.1.554.3993 }} *{{cite journal | first1 = Siddhartha | last1 = Chib | author1-link = Siddhartha Chib | first2 = Edward | last2 = Greenberg | title = Understanding the Metropolis–Hastings Algorithm | journal = The American Statistician | volume = 49 | issue = 4 | pages = 327β335 | year = 1995 | doi = 10.1080/00031305.1995.10476177 | jstor = 2684568 }} *{{cite journal | first1 = A.E. | last1 = Gelfand | first2 = A.F.M. | last2 = Smith | title = Sampling-Based Approaches to Calculating Marginal Densities | journal = [[Journal of the American Statistical Association]] | volume = 85 | issue = 410 | pages = 398β409 | year = 1990 | doi=10.1080/01621459.1990.10476213 | citeseerx = 10.1.1.512.2330 }} *{{cite book | first1 = Andrew | last1 = Gelman | author1-link = Andrew Gelman | first2 = John B. | last2 = Carlin | first3 = Hal S. | last3 = Stern | first4 = Donald B. | last4 = Rubin | author4-link = Donald B. Rubin | title = Bayesian Data Analysis | publisher = [[Chapman and Hall]] | edition = 1st | year = 1995 }} ''(See Chapter 11.)'' *{{cite journal | first1 = S. | last1 = Geman | first2 = D. | last2 = Geman | author2-link = Donald Geman | title = Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images | journal = [[IEEE Transactions on Pattern Analysis and Machine Intelligence]] | volume = 6 | issue = 6 | pages = 721β741 | year = 1984 | doi = 10.1109/TPAMI.1984.4767596 | pmid = 22499653 | s2cid = 5837272 }} *{{cite book | last1 = Gilks | first1 = W.R. | last2 = Richardson | first2 = S. | first3 = D.J. | last3 = Spiegelhalter | author3-link = David Spiegelhalter | title = Markov Chain Monte Carlo in Practice | publisher = [[Chapman and Hall]]/CRC | year = 1996 }} *{{cite book | first = Jeff | last = Gill | title = Bayesian methods: a social and behavioral sciences approach | edition = 2nd | year = 2008 | publisher = [[Chapman and Hall]]/CRC | isbn = 978-1-58488-562-7 }} *{{cite journal | first = P.J. | last = Green | title = Reversible-jump Markov chain Monte Carlo computation and Bayesian model determination | journal = [[Biometrika]] | volume=82 | issue = 4 | pages = 711β732 | year = 1995 | doi = 10.1093/biomet/82.4.711 | citeseerx = 10.1.1.407.8942 }} *{{cite journal | first = Radford M. | last = Neal | title = Slice Sampling | journal = [[Annals of Statistics]] | volume = 31 | issue = 3 | pages = 705β767 | year = 2003 | jstor = 3448413 | doi=10.1214/aos/1056562461 | doi-access = free }} *{{cite web | last = Neal | first = Radford M. | url = http://www.cs.utoronto.ca/~radford/review.abstract.html | title = ''Probabilistic Inference Using Markov Chain Monte Carlo Methods'' | year = 1993 }} *{{cite book |first1 = Christian P. |last1 = Robert |last2 = Casella |first2 = G. |title = Monte Carlo Statistical Methods |url = https://archive.org/details/springer_10.1007-978-1-4757-4145-2 |edition = 2nd |year = 2004 |publisher = Springer |isbn = 978-0-387-21239-5 }} *{{cite book | first1 = R.Y. | last1 = Rubinstein | first2 = D.P. | last2 = Kroese |author-link2=Dirk Kroese | title = Simulation and the Monte Carlo Method | edition = 2nd | publisher = [[John Wiley & Sons|Wiley]] | year = 2007 | isbn = 978-0-470-17794-5 }} *{{cite journal | first = R.L. | last = Smith | title = Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed Over Bounded Regions | journal = [[Operations Research: A Journal of the Institute for Operations Research and the Management Sciences|Operations Research]] | volume = 32 | issue = 6 | pages = 1296β1308 | year = 1984 | doi = 10.1287/opre.32.6.1296 | hdl = 2027.42/7681 | hdl-access = free }} * {{cite journal | first = J.C. | last = Spall | title = Estimation via Markov Chain Monte Carlo | journal = [[IEEE Control Systems Magazine]] | volume = 23 | issue = 2 | pages = 34β45 |date=April 2003 | doi=10.1109/mcs.2003.1188770 }} *{{cite journal | last1 = Stramer | first1 = O. | last2 = Tweedie | first2 = R. | year = 1999 | title = Langevin-Type Models II: Self-Targeting Candidates for MCMC Algorithms | journal = Methodology and Computing in Applied Probability | volume = 1 | issue = 3 | pages = 307β328 | doi = 10.1023/A:1010090512027 | s2cid = 1512689 }} {{refend}}
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