During his talk on unbiased MCMC in Dauphine today, Pierre Jacob provided a nice illustration of the convergence modes of MCMC algorithms. With the stationary target achieved after 100 Metropolis iterations, while the mean of the target taking much more iterations to be approximated by the empirical average. Plus a nice connection between coupling time and convergence. Convergence to the target.
During Pierre’s talk, some simple questions came to mind, from developing an “impatient user version”, as in perfect sampling, in order to stop chains that run “forever”, to optimising parallelisation in order to avoid problems of asynchronicity. While the complexity of coupling increases with dimension and the coupling probability goes down, the average coupling time varies but an unexpected figure is that the expected cost per iteration is of 2 simulations, irrespective of the chosen kernels. Pierre also made a connection with optimal transport coupling and stressed that the maximal coupling was for the proposal and not for the target.
Archive for unbiased MCMC
convergences of MCMC and unbiasedness
Posted in pictures, Statistics, University life with tags asynchronous algorithms, Hastings-Metropolis sampler, impatient user, maximal coupling, MCMC convergence, optimal transport, parallelisation, Paris Dauphine, perfect sampling, unbiased MCMC on January 16, 2018 by xi'anBetter together in Kolkata [slides]
Posted in Books, pictures, Statistics, Travel, University life with tags approximate Bayesian inference, Bayesian inference, better together, dinosaur, India, ISI, k-mean clustering algorithm, Kolkata, MCMC, misspecified model, modularisation, P.C. Mahalanobis, safe Bayes, slideshare, SMC, unbiased MCMC on January 4, 2018 by xi'an
Here are the slides of the talk on modularisation I am giving today at the PC Mahalanobis 125 Conference in Kolkata, mostly borrowed from Pierre’s talk at O’Bayes 2018 last month:
[which made me realise Slideshare has discontinued the option to update one’s presentation, forcing users to create a new presentation for each update!] Incidentally, the amphitheatre at ISI is located right on top of a geological exhibit room with a reconstituted Barapasaurus tagorei so I will figuratively ride a dinosaur during my talk!
