Archive for delayed acceptance

IMS workshop [day 5]

Posted in Books, pictures, Statistics, Travel with tags , , , , , , , , on September 3, 2018 by xi'an

The last day of the starting workshop [and my last day in Singapore] was a day of importance [sampling] with talks by Matti Vihola opposing importance sampling and delayed acceptance and particle MCMC, related to several papers of his that I missed. To be continued in the coming weeks at the IMS, which is another reason to regret having to leave that early [as my Parisian semester starts this Monday with an undergrad class at 8:30!]

And then a talk by Joaquín Miguez on stabilizing importance sampling by truncation which reminded me very much of the later work by Andrew Gelman and Aki Vehtari on Pareto smoothed importance sampling, with further operators adapted to sequential settings and the similar drawback that when the importance sampler is poor, i.e., when the simulated points are all very far from the centre of mass, no amount of fudging with the weights will bring the points closer. AMIS made an appearance as a reference method, to be improved by this truncation of the weights, a wee bit surprising as it should bring the large weights of the earlier stages down.

Followed by an almost silent talk by Nick Whiteley, who having lost his voice to the air conditioning whispered his talk in the microphone. Having once faced a lost voice during an introductory lecture to a large undergraduate audience, I could not but completely commiserate for the hardship of the task. Although this made the audience most silent and attentive. His topic was the Viterbi process and its parallelisation, by using a truncated horizon (presenting connection with overdamped Langevin, eg Durmus and Moulines and Dalalyan).

And due to a pressing appointment with my son and his girlfriend [who were traveling through Singapore on that day] for a chili crab dinner on my way to the airport, I missed the final talk by Arnaud Doucet, where he was to reconsider PDMP algorithms without the continuous time layer, a perspective I find most appealing!

Overall, this was a quite diverse and rich [starting] seminar, backed by the superb organisation of the IMS and the smooth living conditions on the NUS campus [once I had mastered the bus routes], which would have made much more sense for me as part of a longer stay, which is actually what happened the previous time I visited the IMS (in 2005), again clashing with my course schedule at home… And as always, I am impressed with the city-state of Singapore, for the highly diverse food scene in particular, but also this [maybe illusory] impression of coexistence between communities. And even though the ecological footprint could certainly be decreased, measures to curb car ownership (with a 150% purchase tax) and use (with congestion charges).

MCMC with multiple tries

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , on April 5, 2018 by xi'an

Earlier this year, Luca Martino wrote and arXived a review on multiple try MCMC. As its name suggests, the starting point of this algorithm is to propose N potential moves simultaneously instead of one, possibly according to N different proposal (conditional) densities, and to select one by a normalised importance sampling weight. The move is accepted by a Metropolis-Hastings step based on the ratio of the normalisation constants [at the current and at the one-before-current stages]. Besides the cost of computing the summation and generating the different variates, this method also faces the drawback of requiring N-1 supplementary simulations that are only used for achieving detailed balance and computing a backward summation of importance weights. (A first section of the review is dedicated to independent Metropolis-Hastings proposals, q(θ), which make life simpler, but are less realistic in my opinion since some prior knowledge or experimentation is necessary to build a relevant distribution q(θ).) An alternative covered in the survey is ensemble Monte Carlo (Neal, 2011), which produces a whole sample at each iteration, with target the product of the initial targets. This reminded me of our pinball sampler, which aimed at producing a spread-out sample while keeping the marginal correct. Although the motivation sounds closer to a particle sampler. Especially with this associated notion of an empirical approximation of the target. The next part of the review is about delayed rejection, which is a natural alternative approach to speeding up MCMC by considering several possibilities, if sequentially. Started in Antonietta Mira‘s 1999 PhD thesis. The difficulty with this approach is that the acceptance probability gets increasingly complex as the number of delays grows, which may annihilate its appeal relative to simultaneous multiple tries.

delayed acceptance ABC-SMC

Posted in pictures, Statistics, Travel with tags , , , , , , , on December 11, 2017 by xi'an

Last summer, during my vacation on Skye,  Richard Everitt and Paulina Rowińska arXived a paper on delayed acceptance associated with ABC. ArXival that I missed, then! In order to decrease the number of simulations from the likelihood. As in our own delayed acceptance paper (without ABC), a cheap alternative generator is used to first reject the least likely parameters values, before possibly continuing to use a full generator. Also as lazy ABC. The first step of this ABC algorithm requires a cheap generator plus a primary tolerance ε¹ to compare the generation with the data or part of it. This may be followed by a second generation with a second tolerance level ε². The paper applies more specifically ABC-SMC as introduced in Sisson, Fan and Tanaka (2007) and reassessed in our subsequent 2009 Biometrika paper with Mark Beaumont, Jean-Marie Cornuet and Jean-Michel Marin. As well as in the ABC-SMC paper by Pierre Del Moral and Arnaud Doucet.

When looking at the version of the algorithm [Algorithm 2] based on two basic acceptance ABC steps, there are two features I find intriguing: (i) the primary step uses a cheap generator to reject early poor values of the parameter, followed by the second step involving a more expensive and exact generator, but I see no impact of the choice of this cheap generator in the acceptance probability; (ii) this is an SMC algorithm with imposed resampling at each iteration but there is no visible step for creating new weights after the resampling step. In the current presentation, it sounds like the weights do not change from the initial step, except for those turning to zero and the renormalisation transforms. Which makes the (unspecified) stratification of little interest if any. I must therefore miss a point in the implementation!

One puzzling sentence in the appendix is that the resampling algorithm used in the SMC step “ensures that every particle that is alive before resampling is represented in the resampled particles”, which reminds me of an argument [possibly a different one] made already in Sisson, Fan and Tanaka (2007) and that we could not validate in our subsequent paper. For resampling to be correct, a form of multinomial sampling must be implemented, even via variance reduction schemes like stratified or systematic sampling.

computer strategies for complex Bayesian models

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , on July 18, 2016 by xi'an

frontThis is the cover page of Marco Banterle‘s thesis, who will defend on Thursday [July 21, 13:00], at a rather quiet time for French universities, which is one reason for advertising it here. The thesis is built around several of Marco’s papers, like delayed acceptance, dimension expansion, and Gaussian copula for graphical models. The defence is open to everyone, so feel free to join if near Paris-Dauphine!

Monte Carlo in the convent

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , on July 14, 2016 by xi'an

Last week, at the same time as the workshop on retrospective Monte Carlo in Warwick, there was a Monte Carlo conference in Paris, closing a Monte Carlo cycle run by Institut Louis Bachelier from October 2015 till June 2016. It took place in the convent of Les Cordeliers, downtown Paris [hence the title] and I alas could not attend the talks. As I organised a session on Bayesian (approximate) computations, with Richard Everitt, Jere Koskela, and Chris Sherlock as speakers (and Robin Ryder as chair), here are the slides of the speakers (actually, Jere most kindly agreed to give Chris’ talk as Chris was to sick to travel to Paris):