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 SMC
The next MCMSki meeting, MCMSki IV, will be held in Chamonix Mont-Blanc, France, from Monday, January 6 to Wednesday, January 8, 2014. As for the previous MCMSki meetings, it jointly supported by the IMS (Institute of Mathematical Statistics) and ISBA (International Society for Bayesian Analysis), as the first meeting of the newly created BayesComp section of ISBA. It will focus on all aspects of MCMC theory and methodology, including related fields like sequential Monte Carlo, approximate Bayesian computation, Hamiltonian Monte Carlo. In contrast with the earlier meetings, it will merge the satellite Adap’ski workshop into the main meeting by having parallel (invited and contributed) sessions on those different themes. A call for proposals of sessions and talks is available here. There will be also opportunities for presenting one’s work at plenary and well-attended evening poster sessions.
In terms of location, after an excursion to Utah, MCMSki IV is back in the Alps, on the French side of Mont-Blanc, and Chamonix offers a wide range of outdoor and indoor activities during the breaks, with all levels of skiing available. The meeting will take place at the Conference Centre le Majestic (Centre des Congrès – Le Majestic) in Chamonix Mont-Blanc. (With a large population of English expatriates living there, Chamonix is very easy to handle for English speakers. The lodging capacities are both diverse and plenty.)
Carlo Albert and Hans Kuensch recently posted an arXiv paper which provides a new perspective on ABC. It relates to ABC-MCMC and to ABC-SMC in different ways, but the major point is to propose a sequential schedule for decreasing the tolerance that ensures convergence. Although there exist other proofs of convergence in the literature, this one is quite novel in that it connects ABC with the cooling schedules of simulated annealing. (The fact that the sample size does not appear as in Fearnhead and Prangle and their non-parametric perspective can be deemed less practical, but I think this is simply another perspective on the problem!) The corresponding ABC algorithm is a mix of MCMC and SMC in that it lets a population of N particles evolve in a quasi-independent manner, the population being only used to update the parameters of the independent (normal) proposal and those of the cooling tolerance. Each particle in the population moves according to a Metropolis-Hastings step, but this is not an ABC-MCMC scheme in that the algorithm works with a population at all times, and this is not an ABC-SMC scheme in that there is no weighting and no resampling.
Maybe I can add two remarks about the conclusion: the authors do not seem aware of other works using other penalties than the 0-1 kernel, but those abound, see e.g. the discussion paper of Fearnhead and Prangle. Or Ratmann et al. The other missing connection is about adaptive tolerance construction, which is also found in the literature, see e.g. Doucet et al. or Drovandi and Pettitt.
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!)
Our (ANR) research project BANDHIT (which stands for Bayesian nonparametrics, high dimensional techniques and simulation, so there is no spelling mistake!) is calling for applicants to a one-year postdoc position. The themes are highly exciting: Bayesian nonparametrics, simulation techniques like MCM, SMC and of course ABC! Here is the full call:
We are seeking accomplished applicants for a post-doctoral research associate position. Candidates must hold a PhD in mathematical or computational statistics, and the ideal candidate will have research experience in theoretical properties of Bayesian nonparametric statistics, MCMC or SMC algorithms or nonparametric estimation. The associate will work with several members of the BANDHITS (Bayesian nonparametrics, high dimensional techniques and simulation) research project which includes statisticians from several universities in Paris (Paris-Dauphine, CREST-ENSAE, Paris 6, Paris 7, University Paris-Sud (Orsay), and CEA). The associate will be expected to participate in research leading to publications in top journals. The appointment, which can begin immediately, will be for a one-year contract. Applicants should email their vita, a brief statement of their background and interests to Judith Rousseau, rousseau[chez]ceremade[dot]dauphine[dot]fr