**A** few days ago I found on the page Jeff Rosenthal has dedicated to Hastings that he has passed away peacefully on May 13, 2016 in Victoria, British Columbia, where he lived for 45 years as a professor at the University of Victoria. After holding positions at University of Toronto, University of Canterbury (New Zealand), and Bell Labs (New Jersey). As pointed out by Jeff, Hastings’ main paper is his 1970 Biometrika description of Markov chain Monte Carlo methods, Monte Carlo sampling methods using Markov chains and their applications. Which would take close to twenty years to become known to the statistics world at large, although you can trace a path through Peskun (his only PhD student) , Besag and others. I am sorry it took so long to come to my knowledge and also sorry it apparently went unnoticed by most of the computational statistics community.

## Archive for Peskun ordering

## Wilfred Keith Hastings [1930-2016]

Posted in Books, Mountains, pictures, Statistics, Travel, University life with tags Bell Labs, Biometrika, Canada, Julian Besag, Metropolis-Hastings algorithm, obituary, Peskun ordering, University of Canterbury, University of Victoria, Victoria, Wilfred Keith Hastings on December 9, 2016 by xi'an## accelerating Metropolis-Hastings algorithms by delayed acceptance

Posted in Books, Statistics, University life with tags Andrew Gelman, Hamiltonian Monte Carlo, MALA, Metropolis-Hastings algorithm, Montréal, NIPS, Peskun ordering, prefetching, University of Warwick on March 5, 2015 by xi'an**M**arco Banterle, Clara Grazian, Anthony Lee, and myself just arXived our paper “Accelerating Metropolis-Hastings algorithms by delayed acceptance“, which is an major revision and upgrade of our “Delayed acceptance with prefetching” paper of last June. Paper that we submitted at the last minute to NIPS, but which did not get accepted. The difference with this earlier version is the inclusion of convergence results, in particular that, while the original Metropolis-Hastings algorithm dominates the delayed version in Peskun ordering, the later can improve upon the original for an appropriate choice of the early stage acceptance step. We thus included a new section on optimising the design of the delayed step, by picking the optimal scaling à la Roberts, Gelman and Gilks (1997) in the first step and by proposing a ranking of the factors in the Metropolis-Hastings acceptance ratio that speeds up the algorithm. The algorithm thus got adaptive. Compared with the earlier version, we have not pursued the second thread of prefetching as much, simply mentioning that prefetching and delayed acceptance could be merged. We have also included a section on the alternative suggested by Philip Nutzman on the ‘Og of using a growing ratio rather than individual terms, the advantage being the probability of acceptance stabilising when the number of terms grows, with the drawback being that expensive terms are not always computed last. In addition to our logistic and mixture examples, we also study in this version the MALA algorithm, since we can postpone computing the ratio of the proposals till the second step. The gain observed in one experiment is of the order of a ten-fold higher efficiency. By comparison, and in answer to one comment on Andrew’s blog, we did not cover the HMC algorithm, since the preliminary acceptance step would require the construction of a proxy to the acceptance ratio, in order to avoid computing a costly number of derivatives in the discretised Hamiltonian integration.

## Carlin and Chib (1995) for fixed dimension problems

Posted in Books, Kids, Statistics, University life with tags asbestos, Brad Carlin, Jussieu, Paris, Peskun ordering, PhD thesis, pseudo-priors, Sid Chib, Université Pierre et Marie Curie on February 25, 2014 by xi'an**Y**esterday, I was part of a (public) thesis committee at the Université Pierre et Marie Curie, in down-town Paris. After a bit of a search for the defence room (as the campus is still undergoing a massive asbestos clean-up, 20 years after it started…!), I listened to Florian Maire delivering his talk on an array of work in computational statistics ranging from the theoretical (Peskun ordering) to the methodological (Monte Carlo online EM) to the applied (unsupervised learning of classes shapes via deformable templates). The implementation of the online EM algorithm involved the use of pseudo-priors à la Carlin and Chib (1995), even though the setting was a fixed-dimension one, in order to fight the difficulty of exploring the space of templates by a regular Gibbs sampler. (As usual, the design of the pseudo-priors was crucial to the success of the method.) The thesis also included a recent work with Randal Douc and Jimmy Olsson on ranking inhomogeneous Markov kernels of the type

against alternatives with components (P’,Q’). The authors were able to characterise minimal conditions for a Peskun-ordering domination on the components to transfer to the combination. Quite an interesting piece of work for a PhD thesis!

## snapshot from Budapest (EMS 20130 #1)

Posted in pictures, Running, Statistics, Travel, University life with tags Bayesian nonparametrics, Buda, EMS 2013, Hungary, Peskun ordering on July 23, 2013 by xi'an**I** had a nice “working” day in Budapest today, spending most of the time looking at Markov chain diagrams and Peskun orderings with Randal Douc, while drinking litres of iced coffee, meaning I skipped a large part of the talks at EMS 2013 I am afraid… Thanks to the very early sunrise in Budapest (which is on the same time zone as Brest or even Porto!), I managed to have a long run along the Danube and a breakfast with my friends Gautami and Peter before the conference had even started. I still attended David Balding’s invited talk on DNA based evidence, containing an illustration in the Amanda knox case, the Bayesian non-parametric session, which provided me with additional illustrations for The Talk, from Bernstein-von Mises to species estimation, then the computational biology session where Michael Stumpf showed us a masterly mix of stick breaking processes, Bayesian networks, hidden Markov models and genetics. And… we managed to make considerable progress in this proof of ours!

## Reading classics (#5)

Posted in Books, Statistics, University life with tags Biometrika, David Cox, Hastings, Markov chain Monte Carlo, Metropolis-Hastings, Mike Titterington, Monte Carlo Statistical Methods, numerical integration, Peskun ordering, simulation on December 14, 2012 by xi'an**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.

## Monte Carlo Statistical Methods third edition

Posted in Books, R, Statistics, University life with tags Bayesian lasso, hierarchical Bayesian modelling, Introducing Monte Carlo Methods with R, Markov chains, MCMC, mixture estimation, Monte Carlo Statistical Methods, nested sampling, perfect sampling, Peskun ordering, R, Rao-Blackwellisation, regeneration, slice sampling on September 23, 2010 by xi'an**L**ast week, George Casella and I worked around the clock on starting the third edition of * Monte Carlo Statistical Methods* by detailing the changes to make and designing the new table of contents. The new edition will not see a revolution in the presentation of the material but rather a more mature perspective on what matters most in statistical simulation: