Archive for MCQMC

accelerated ABC

Posted in Books, Mountains, Statistics with tags , , , , , , on January 14, 2014 by xi'an

Richard Wilkinson arXived a paper on accelerated ABC during MCMSki 4, paper that I almost missed when quickly perusing the daily list. This is another illustration of the “invasion of Gaussian processes” in ABC settings. Maybe under the influence of machine learning.

The paper starts with a link to the synthetic likelihood approximation of Wood (2010, Nature), as in Richard Everitt’s talk last week. Richard (W.) presents the generalised ABC as a kernel-based acceptance probability, using a kernel π(y|x), when y is the observed data and x=x(θ) the simulated one. He proposes a Gaussian process modelling for the log-likelihood (at the observed data y), with a quadratic (in θ) mean and Matérn covariance matrix. Hence the connection with Wood’s synthetic likelihood. Another connection is with Nicolas’ talk on QMC(MC): the θ’s are chosen following a Sobol sequence “in order to minimize the number of design points”. Which requires a reparameterisation to [0,1]p… I find this “uniform” exploration of the whole parameter space delicate to envision in complex parameter spaces and realistic problems, since the likelihood is highly concentrated on a tiny subregion of the original [0,1]p. Not mentioning the issue of the spurious mass on the boundaries of the hypercube possibly induced by the change of variable. The sequential algorithm of Richard also attempts at eliminating implausible zones of the parameter space. i.e. zones where the likelihood is essentially zero. My worries with this interesting notion are that (a) the early Gaussian process approximations may be poor and hence exclude zones they should not; (b) all Gaussian process approximations at all iterations must be saved; (c) the Sobol sequences apply to the whole [0,1]p at each iteration but the non-implausible region shrinks at each iteration, which induces a growing inefficiency in the algorithm. The Sobol sequence should be restricted to the previous non-implausible zone.

Overall, an interesting proposal that would need more prodding to understand whether or not it is robust to poor initialisation and complex structures. And a proposal belonging to the estimated likelihood branch of ABC, which makes use of the final Gaussian process approximation to run an MCM algorithm. Without returning to pseudo-data simulation, replacing it with log-likelihood simulation.

“These algorithms sample space randomly and naively and do not learn from previous simulations”

The above criticism is moderated in a footnote about ABC-SMC using the “current parameter value to determine which move to make next [but] parameters visited in previous iterations are not taken into account”. I still find it excessive in that SMC algorithms and in particular ABC-SMC algorithms are completely free to use the whole past to build the new proposal. This was clearly enunciated in our earlier population Monte Carlo papers. For instance, the complete collection of past particles can be recycled by weights computing thru our AMIS algorithm, as illustrated by Jukka Corander in one genetics application.

9th IMACS seminar on Monte Carlo Methods, Annecy

Posted in Mountains, pictures, R, Running, Statistics, Travel, University life with tags , , , , , , , , , , on July 18, 2013 by xi'an

IMG_0361As astute ‘Og’s readers may have gathered (!), I am now in Annecy, Savoie, for the 9th IMACS seminar on Monte Carlo Methods. Where I was kindly invited to give a talk on ABC. IMACS stands for “International Association for Mathematics and Computers in Simulation” and the conference gathers themes and sensibilities I am not familiar with. And very few statisticians. For instance, I attended a stochastic particle session that had nothing to do with my understanding of particle systems (except for Pierre Del Moral’s mean field talk). The overall focus seems to stand much more around SDEs and quasi-Monte Carlo methods. Both items for which I have a genuine interest but little background, so I cannot report much on the talks I have attended beyond reporting their title. I for instance discovered the multilevel Monte Carlo techniques for SDEs, which sounds like a control variate methodology to reduce the variance w/o reducing the discretisation step. (Another instance is that the proceedings will be published in Mathematics and Computers in Simulation or Monte Carlo Methods and Applications. Two journals I have never published in.) Although I have yet a few months before attending my first MCQMC conference, I presume this is somehow a similar spirit and mix of communities.

IMG_0392At another level, attending a conference in Annecy is a blessing: the city is beautiful, the lake pristine and tantalising in the hot weather, and the surrounding mountains (we are actually quite close to Chamonix!) induce me to go running on both mornings and evenings.

MCQMC 2012

Posted in Statistics with tags , , , , , on January 26, 2011 by xi'an

Just received today the announcement for the next MCQMC meeting, which will be the 10th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2012), taking place in Sydney from February 13 to 17, 2012.

MCQMC is a biennial conference devoted to Monte Carlo and quasi-Monte Carlo methods and their interactions and applications.  (In brief, quasi-Monte Carlo methods replace the random choices that characterize the Monte Carlo method by well chosen deterministic choices.)  For more information, click on the “Background” tab on the web site.  This will be the first MCQMC conference to be held in the southern hemisphere.  (Northerners may like to be reminded that February is summertime in Sydney!)

The invited plenary speakers for MCQMC are
* Pierre Del Moral (INRIA & University of Bordeaux 1, France)
* Mike Giles (University of Oxford, UK)
* Fred J. Hickernell (Illinois Institute of Technology, USA)
* Aicke Hinrichs (University of Jena, Germany)
* Michael Lacey (Georgia Institute of Technology, USA)
* Kerrie Mengersen (Queensland University of Technology, Australia)
* Andreas Neuenkirch (University of Kaiserslautern, Germany)
* Art B. Owen (Stanford University, USA)
* Leszek Plaskota (University of Warsaw, Poland)
* Eckhard Platen (University of Technology Sydney, Australia)

Proposals for special sessions should contain
* a short description of the theme and scope of the session
* the name(s) of the organizer(s)
* the names of four speakers (preferably from different institutions)
who have agreed to participate
The deadline for submitting proposals is July 1, 2011.  There will be a later call for contributed talks.

Please join us for MCQMC


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