ISC-5939-03

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Markov Chain Monte Carlo in Practice Seminar

We will read and discuss papers on MCMC and also look at implementation of these methods in real world applications (Material Science, Geology, and Evolution).

Class meeting is on Mondays 2-3pm in room 499.

Wikipedia: Metropolis-Hastings algorithm
EXAMPLE CODES IN PYTHON. Currently there are two files that give an example of the Metropolis method (using a symmetric proposal) and an example that showcases the Metropolis-Hastings method (using an asymmetric proposal that needs the Hastings ratio correction). You can tinker with the second one by setting a flag to evaluate the Metropolis method with this asymetric proposal. Of course, this gives a horrible result.


February 3 2014 Sachin Shanbhag will lead the discussion of M. Rosenbluth and A. Rosenbluth (1955). Monte Carlo Calculation of the Average Extension of Molecular Chains. Journal of Chemical Physics 23(2):356-359. [media:rosenbluth_1955.pdf PDF]]

January 13/27 2014 Peter Beerli will present the program MIGRATE and discuss implementation of the algorithms. [media:beerli_1999.pdf PDF]]

November 25 Roger Pacheco Castro will lead: Green, P., J. (1995). Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination. Biometrika 82(4): 711-732. PDF

November 18 Ben McLaughlin will lead: Kass, R.E. et al., 1998. Markov Chain Monte Carlo in Practice: A Roundtable Discussion. The American Statistician, 52(2): 93–100. PDF

November 4 Hans-Werner van Wyk will lead: Gelman, A. & Rubin, D., 1992. Inference from Iterative Simulation Using Multiple Sequences. Statistical Science 7:457-472. PDF. A key paper to compare multiple chains using the same stationary distribution, used to establish convergence.

October 28 Aretha Teckentrup will lead: C. Ketelsen, R. Scheichl and A.L. Teckentrup . A Hierarchical Multilevel Markov chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow.. Submitted March 2013, available as arXiv:1303.7343 preprint, or directly from Aretha's website (PDF)

October 21 James Cheung will lead: Neal, R. (2003) Slice Sampling. Annals of Statistics 31(3):705-767. PDF. This is a Gibbs sampler, but it is often easier to use than a standard Gibbs sampler.

October 14 Feifei Xu will lead: Geman, S. and D. Geman (1984) Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. PAMI-6, NO. 6: 721-741 PDF, this paper is rather technical, it will help to compare it to the paper by Casella, G. and E. I. George [1992] Explaining the Gibbs sampler. The American Statistician 46(3): 167-174 PDF, which is easier to recognize the MCMC theme.

September 30 Sachin Shanbhag will lead: Marinari, E. and G. Parisi (1992). Simulated Tempering: A New Monte Carlo Scheme. Europhys. Lett., 19 (6): 451-458 download PDF

September 23 Peter Beerli will lead: Geyer C. J. and E. A. Thompson (1995) Annealing Markov Chain Monte Carlo with Applications to Ancestral Inference. download PDF You definitely want to visit Charlie Geyer's website and specifically his rant about on long chains and burn-in of MCMC.

September 16 Sachin Shanbhag will lead: W. K. Hastings (1970) Monte Carlo Sampling Methods Using Markov Chains and Their Applications. Biometrika 57(1):97-109. download PDF EXAMPLE CODE IN PYTHON)

September 9 Peter Beerli will lead.

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We will all read this paper and discuss their approach: interesting topics are assumptions, run time, number of evaluation etc.(download PDF, EXAMPLE CODE IN PYTHON)

Here are some more tidbits from the early MCMC times: first textbook by Hammersley and Handscomb (1962) PDF, news from the Los Alamos Science: The Beginning of the Monte Carlo method, Computing and Computers