As I was checking the recent stat postings on arXiv, I noticed the paper by Chen and Xie entitled inference in Kingman’s coalescent with pMCMC. (And surprisingly deposited in the machine learning subdomain.) The authors compare a pMCMC implementation for Kingman’s coalescent with importance sampling (à la Stephens & Donnelly), regular MCMC and SMC. The specifics of their pMCMC algorithm is that they simulate the coalescent times conditional on the tree structure and the tree structure conditional on the coalescent times (via SMC). The results reported in the paper consider up to five loci and agree with earlier experiments showing poor performances of MCMC algorithms (based on the LAMARC software and apparently using independent proposals). They show similar performances between importance sampling and pMCMC. While I find this application of pMCMC interesting, I wonder at the generality of the approach: when I was introduced to ABC techniques, the motivation was that importance sampling was deteriorating very quickly with the number of parameters. Here it seems the authors only considered one parameter θ. I wonder what happens when the number of parameters increases. And how pMCMC would then compare with ABC.
Archive for pMCMC
inference in Kingman’s coalescent with pMCMC
Posted in Books, Statistics, University life with tags ABC, Gibbs sampling, importance sampling, Kingman's coalescent, pMCMC, population genetics, simulation, SMC on May 22, 2013 by xi'anMCMSki IV in Chamonix-Mont-Blanc, Jan. 6-8, 2014!!!
Posted in Mountains, Statistics, Travel, University life with tags ABC, Adapski, Alps, Chamonix, conference, MCMC, MCMSki, Mont Blanc, pMCMC, ski, SMC on July 23, 2012 by xi'an
As mentioned a few days ago (in tragic circumstances), the fourth MCMSki meeting will take place in Chamonix-Mont-Blanc on January 6-8, 2014. It will actually be focussing more on methodological and theoretical issues about MCMC (and SMC and ABC and…) than on its applications and so it supersedes both the Adap’ski and MCMCSki earlier meetings. It will (hopefully) be sponsored by statistical societies, including ISBA and IMS, as in the earlier instances. We are still discussing with the Conference Centre in Chamonix about the details, but I think the registration costs will remain quite reasonable (around 120-150 euros), with a wide range of accomodation available in Chamonix and around, and of course an unbelievable skiing domain. The webpage should come to life in a few days, after Antonietta Mira, Brad Carlin and myself complete the scientific and the organisation committees. So… make sure to keep this first week of 2014 free in your agendas! (And for those worried about transportation, Geneva international airport is only 88k away, with an expressway all the way to Chamonix. With plenty of shuttles if you do not want to rent a car. There also is a sleeper train from Paris that arrives early enough in the morning to enjoy a full day of mcmskiing!)
ABC and Monte Carlo seminar in CREST
Posted in Statistics, University life with tags ABC, auxiliary variables, CREST, ENSAE, expectation-propagation, MC² algorithm, pMCMC, SMC² on January 13, 2012 by xi'anOn Monday (Jan. 16, 3pm, CREST–ENSAE, Room S08), Nicolas Chopin will present a talk on:
Dealing with intractability: recent advances in Bayesian Monte-Carlo methods for intractable likelihoods
(joint works with P. Jacob, O. Papaspiliopoulos and S. Barthelmé)This talk will start with a review of recent advancements in Monte Carlo methodology for intractable problems; that is problems involving intractable quantities, typically intractable likelihoods. I will discuss in turn ABC type methods (a.k.a. likelihood-free), auxiliary variable methods for dealing with intractable normalising constants (e.g. the exchange algorithm), and MC² type of algorithms, a recent extension of which being the PMCMC algorithm (Andrieu et al., 2010). Then, I will present two recent pieces of work in these direction. First, and more briefly briefly, I’ll present the ABC-EP algorithm (Chopin and Barthelmé, 2011). I’ll also discuss some possible future research in ABC theory. Second, I’ll discuss the SMC² algorithm (Chopin, Jacob and Papaspiliopoulos, 2011), a new type of MC² algorithm that makes it possible to perform sequential analysis for virtually any state-space models, including models with an intractable Markov transition.
MCMC with errors
Posted in R, Statistics, University life with tags ABC, Annals of Statistics, Columbia University, MCMC, Metropolis-Hastings, Monte Carlo Statistical Methods, particle filters, pMCMC on March 25, 2011 by xi'anI received this email last week from Ian Langmore, a postdoc in Columbia:
I’m looking for literature on a subject and can’t find it: I have a Metropolis sampler where the acceptance probability is evaluated with some error. This error is not simply error in evaluation of the target density. It occurs due to the method by which we approximate the acceptance probability.
This is a sensible question, albeit a wee vague… The closest item of work I can think of is the recent paper by Christophe Andrieu and Gareth Roberts, in the Annals of Statistics (2009) following an original proposal by Marc Beaumont. I think there is an early 1990’s paper by Gareth and Jeff Rosenthal where they consider the impact of some approximation effect like real number representation on the convergence but I cannot find it. Of course, the recent particle MCMC JRSS B discussion paper by Christophe, Arnaud Doucet and Roman Hollenstein is a way to bypass the problem. (In a sense ABC is a rudimentary answer as well.) And there must be many other papers on this topic I am not aware of….
