## Reading classics (#5)

**T**his week, my student Dona Skanji gave a presentation of the paper of Hastings “Monte Carlo sampling methods using Markov chains and their applications“, which set the rules for running MCMC algorithms, much more so than the original paper by Metropolis et al. ~~which presented an optimisation device~~. even though the latter clearly stated the Markovian principle of those algorithms and their use for integration. (This is definitely a classic, selected in the book *Biometrika: One hundred years*, by Mike Titterington and David Cox.) Here are her slides (the best Beamer slides so far!):

**G**iven that I had already taught my lectures on Markov chains and on MCMC algorithms, the preliminary part of Dona’s talk was easier to compose and understanding the principles of the method was certainly more straightforward than for the other papers in the series. I think she nonetheless did a rather good job in summing up the paper, running this extra simulation for the Poisson distribution—with the interesting “mistake” of including the burnin time in the representation of the output and concluding about a poor convergence—and mentioning the Gibbs extension.I led the discussion of the seminar towards irreducibility conditions and Peskun’s ordering of Markov chains, which maybe could have been mentioned by Dona since she was aware Peskun was Hastings‘ student.

December 14, 2012 at 2:15 am

What’s this about Metropolis, et al “presenting an optimization device”? They present the Metropolis algorithm, as it is understood today (with a systematic scan over subsets of coordinates, though the variation in which all coordinates are updated at once is obvious). They develop the algorithm for general continuous distributions, and then apply it to sampling from a uniform distribution on a high-dimensional region defined by a very complex set of constraints. Their goal is integration, not optimization. Indeed, for the application they present, optimization would make no sense.

December 14, 2012 at 7:36 am

Oh, dear!, thanks for setting me right, Radford, and for lifting a misunderstanding of the paper that had stayed with me for a long while. Because Metropolis et al. were using a target that involved a temperature T, I wrongly inferred that they were invented both MCMC and simulated annealing in the same go! I am afraid I propagated this wrong message in several of my papers and books. Thanks!