Markov Chain Monte Carlo in Practice Seminar
[this seminar is currently on hold and may restart in Fall 2016]
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 11-12 in DSL 150-T (Spring 2015).
Wikipedia: Metropolis-Hastings algorithm
Charlie Geyer about MCMC: Why one long run is enough; Burn-in are unnecessary; On the Bogosity of MCMC Diagnostics
Radford Neal on several MCMC topics.
We have successfully implemented several versions of code using reversible jump to fit a polynomial to data. See example section (to come)
February - March 30, 2015
We have looked at simulated annealing (code will come) and have started to discuss reversible jump using Green and Hastie's paper, an implmentation of their example is now in the python examples (see bottom of this page). We will discuss on March 30 the paper by Fan and Brooks: Bayesian Modelling of Prehistoric Corbelled Domes.
February 2, 2015
Presentation of code for the Hamiltonian MCMC, using Neal's code fragment to reproduce his example, and perhaps using our own example (Peter's three-peak function, and Sachin's spring example)
January 26, 2015
Reading Radford Neal's chapter on Hamiltonian MCMC (5.1,5.2,5.3): Radford M. Neal (2010) MCMC using Hamiltonian dynamics', in the Handbook of Markov Chain Monte Carlo, S. Brooks, A. Gelman, G. L. Jones, and X.-L. Meng (editors), Chapman & Hall / CRC Press, pp. 113-162
January 11, 2015
Organization meeting: we meet this semester in DSL 150-T on Mondays 11-12
November 10, 2014
November 2, 2014
Students code the MCMCMC algorithms discussed last time: see the template and the acceptance rejection step for the temperatures (figure)]]. It would be great if two volunteers could come forward (email to Peter).
October 27, 2014
Read Charles Geyer 1991 paper for this session, we will discuss the algorithm for this parallel heating scheme. The paper is very general, and only the section 'New methods' talks about MCMCMC, but read all of it.
October 20, 2014
We talked about number evaluations and drifted off to convergence and MCMCMC,
October 13, 2014
We read Tibbits et al (2014, PDF) and look at student codes
October 6, 2014
We have all read Radford Neal's Slice sampling paper (2003, PDF), we will discuss the approach and will outline an algorithm for our example programs. For high-dimensional slice sampling you may want to read Tibbits et al (2014, PDF)
September 29, 2014
We will discuss solutions to Sachin's exercise, look at Peter's example (see python program) and talk more about the Hasting's ratio.
September 22, 2014
Hastings, W. K.. 1970. Monte Carlo Sampling Methods Using Markov Chains and Their Applications. Biometrika Vol. 57, No. 1. (Apr., 1970), pp. 97-109. PDF
Students will finish the Metropolis program and add the Hastings ratio, check out in the python example, the example allows to turn on and off the Hastings ratio. Sachin Shanbhag showed these slides PDF
Presentations of student programs
September 8, 2014
Some other articles that are relevant for this seminar
Radford M. Neal (2010) MCMC using Hamiltonian dynamics', in the Handbook of Markov Chain Monte Carlo, S. Brooks, A. Gelman, G. L. Jones, and X.-L. Meng (editors), Chapman & Hall / CRC Press, pp. 113-162: abstract, pdf, associated software.
Grassberger (1997). Pruned-enriched Rosenbluth method: Simulations of $ $ polymers of chain length up to 1 000 000. PHYSICAL REVIEW E 56(3):3682-3693. PDF
M. Rosenbluth and A. Rosenbluth (1955). Monte Carlo Calculation of the Average Extension of Molecular Chains. Journal of Chem.... Media:Rosenbluth_1955.pdf
Harlow FH, N Metropolis 1983. Computing and Computers: Weapons Simulation Leads to the Computer Era. PDF
N Metropolis 1983. The Beginning of the Monte Carlo Method. PDF
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.
to be extended ....