Archive for Columbia University

WSC [2]011

Posted in Mountains, pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , on December 15, 2011 by xi'an

Last day at WSC 2011: as it was again raining, I could not run a second time into the South Mountain Preserve park. (I had a swim at 5am instead and ended up having a nice chat with an old man in the pool under the rain!) My first morning session was rather disappointing with two talks that remained at such a high level of generality as to be useless and a mathematical talk about new forms of stochastic approximation that included proofs and no indication on the calibration of its many parameters. During the coffee break, I tried to have a chat with a vendor of a simulation software but we were using so different vocabularies that I soon gave up. (A lot of the software on display was a-statistical in that users would build a network, specify all parameters, incl. the distributions at the different nodes and start calibrating those parameters towards a behaviour that suited them.) The second session was much more in my area of interest/expertise, with Paul Dupuis giving a talk in the same spirit as the one he gave in New York last September. using large deviations and importance sampling on diffusions. Both following talks were about specially designed importance sampling techniques for rare events and about approximating the zero variance optimal importance function: Yixi Shin gave a talk on cross-entropy based selection of mixtures for the simulation of tail events, connecting somehow with the talk on mixtures of importance sampling distributions I attended yesterday. Although I am afraid I dozed a while during the talk, it was an interesting mix with the determination of the weights by cross-entropy arguments reminded me of what we did for the population Monte Carlo approach (since it also involved some adaptive entropy optimisation). Zdravko Botev gave a talk on approximating the ideal zero variance importance function by MCMC and a sort of Rao-Blackwell estimator that gives an unbiased estimator of this density under stationarity. Then it was time to leave for the airport (and wait in a Starbucks for the plane to Minneapolis and then London to depart, as there is no such thing as a lounge in Phoenix airport…). I had an interesting exchange with a professional magician in the first plane, The Amazing Hondo!, who knew about Persi and was a former math teacher. He explained a few tricks to me, plus showed me his indeed amazing sleight of hands in manipulating cards. In exchange, I took Persi’s book on Magic and Mathematics out of my bag so that he could have look at it. (The trip to London was completely uneventful as I slept most of the way.)

Overall, WSC 2011 was an interesting experience in that (a) the talks I attended on zero variance importance simulation set me thinking again on potential applications of the apparently useless optimality result; (b) it showed me that most people using simulation do not, N.O.T., relate to Monte Carlo techniques (to the extent of being completely foreign to my domains of expertise); and (c) among the parallel sessions that cover military applications, health care simulation, &tc., there always is a theme connecting to mines, which means that I will find sessions to attend when taking part in WSC 2012 in Berlin next year (since I have been invited for a talk). This will be the first time WSC is held outside North America. Hopefully, this will attract simulation addicts from Europe as well as elsewhere.

workshop in Columbia [day 3]

Posted in pictures, R, Running, Statistics, Travel, University life with tags , , , , , , , , , , on September 27, 2011 by xi'an

Although this was only a half-day of talks, the third day of the workshop was equally thought-challenging and diverse.  (I managed to miss the ten first minutes by taking a Line 3 train to 125th street, having overlooked the earlier split from Line 1… Crossing south Harlem on a Sunday morning is a fairly mild experience though.) Jean-Marc Azaïs gave a personal recollection on the work of Mario Wschebor, who passed away a week ago and should have attended the workshop. Nan Chen talked about the Monte Carlo approximation of quantities of the form

\mathbb{E}[f(\mathbb{E}[Y|X])]

which is a problem when f is non linear. This reminded me (and others) of the Bernoulli factory and of the similar trick we use in the vanilla Rao-Blackwellisation paper with Randal Douc. However, the approach was different in that the authors relied on a nested simulation algorithm that did not adapt against f. And did not account for the shape of f. Peter Glynn, while also involved in the above, delivered a talk on the initial transient that showed possibilities for MCMC convergence assessment (even though this is a much less active area than earlier). And, as a fitting conclusion, the conference organiser, Jingchen Liu gave a talk on non-compatible conditionals he and Andrew are using to handle massively-missing datasets. It reminded me of Hobert and Casella (1996, JASA) of course and also of discussions we had in Paris with Andrew and Nicolas. Looking forward to the paper (as I have missed some points about the difference between true and operational models)! Overall, this was thus a terrific workshop (I just wish I could have been able to sleep one hour more each night to be more alert during all talks!) and a fantastic if intense schedule fitting the start of the semester and of teaching (even though Robin had to teach my first R class in English on Friday). I also discovered that several of the participants were attending the Winter Simulation Conference later this year, hence another opportunity to discuss simulation strategies together.

workshop in Columbia [day 2]

Posted in Kids, pictures, Statistics, Travel, University life with tags , , , , on September 26, 2011 by xi'an

The second day at the workshop was closer to my research topics and thus easier to follow, if equally enjoyable compared with yesterday: Jun Liu’s talk went over his modification of the Clifford-Fearnhead particle algorithm in great details, Sam Kou explained how a simulated annealing algorithm could make considerable improvement in the prediction of the 3D structure of molecules, Jeff Rosenthal showed us the recent results on and applications of adaptive MCMC, Gareth Roberts detailed his new results on the exact simulation of diffusions, and Xiao-Li Meng went back to his 2002 Read Paper to explain how we should use likelihood principles in Monte Carlo as well. And convince me I was “too young” to get the whole idea! (As I was a discussant of this paper.) All talks were thought-provoking and I enjoyed very much Gareth’s approach and description of the algorithm (as did the rest of the audience, to the point of asking too many questions during the talk!). However, the most revealing talk was Xiao-Li’s in that he did succeed in convincing me of the pertinence of his “unknown measure” approach thanks to a multiple mixture example where the actual mixture importance sampler

\dfrac{1}{n}\sum_{i=1}^n \dfrac{q(x_i)}{\sum \pi_j p_j(x_i)}

gets dominated by the estimated mixture version

\dfrac{1}{n}\sum_{i=1}^n \dfrac{q(x_i)}{\sum \hat\pi_j p_j(x_i)}

Even though I still remain skeptical by the group averaging perspective, for the same reason as earlier that the group is not acting in conjunction with the target function. Hence averaging over transforms of no relevance for the target. Nonetheless, the idea of estimating the best “importance function” based on the simulated values rather than using the genuine importance function is quite a revelation, linking with an earlier question of mine (and others) on the (lack of) exploitation of the known values of the target at the simulated points. (Maybe up to a constant.) Food for thought, certainly… In memory of this discussion, here is a picture [of an ostrich] my daughter drew at the time for my final slide in London:

workshop in Columbia [talk]

Posted in Statistics, Travel, University life with tags , , , , , , , , , on September 25, 2011 by xi'an

Here are the slides of my talk yesterday at the Computational Methods in Applied Sciences workshop in Columbia:

The last section of the talk covers our new results with Jean-Michel Marin, Natesh Pillai and Judith Rousseau on the necessary and sufficient conditions for a summary statistic to be used in ABC model choice. (The paper is about to be completed.) This obviously comes as the continuation of our reflexions on  ABC model choice started last January. The major message of the paper is that the statistics used for running model choice cannot have a mean value common to both models, which strongly implies using ancillary statistics with different means under each model. (I am afraid that, thanks to the mixture of no-jetlag fatigue and of slide inflation [95 vs. 40mn] and of asymptotics technicalities in the last part, the talk was far from comprehensible. I started on the wrong foot with not getting an XL [Xiao-Li’s] comment on the measure-theory problem with the limit in ε going to zero. A peak given that great debate we had in Banff with Jean-Michel, David Balding, and Mark Beaumont, years ago. And our more recent paper about the arbitrariness of the density value in the Savage-Dickey paradox. I then compounded the confusion by stating the empirical mean was sufficient in the Laplace case…which is not even an exponential family. I hope I will be more articulate next week in Zürich where at least I will not speak past my bedtime!)

Weird moment

Posted in pictures, Travel with tags , on September 25, 2011 by xi'an

As I was waiting at the 86th street station, for a Line 1 subway train to get back to Columbia,  an express Line 2 zoomed by with the usual deafening noise and its whiff of better left unidentified odors… And then, as the train was vanishing into the tunnel, I had the fleeting vision of a red wreath attached to the back door! (As the thing could not be a life-preserver (!) I wonder what it was. Or if I urgently need to check my vision…)

workshop in Columbia

Posted in Statistics, Travel, University life with tags , , , , , , , , , on September 24, 2011 by xi'an

The workshop in Columbia University on Computational Methods in Applied Sciences is quite diverse in its topics.  Reminding me of the conference on Efficient Monte Carlo in Sandbjerg Estate, Sønderborg in 2008, celebrating the 70th birthday of Reuven Rubinstein, incl. some colleagues I had not met since this meeting. Yesterday I thus heard (quite interesting) talks on domains somehow far from my own, from Robert Adler on cohomology (giving a second look  at the thing after the talk I head in Wharton last year), to José Blanchet on simulation for infinite server queues (with a link to perfect sampling I could not exactly trace but that was certainly there). Several of the talks made me think of our Brownian motion confidence band paper, with Wilfrid Kendall and Jean-Michel Marin, esp. Gennady Samorodnitsky’s on the maximum of stochastic processes (and wonder whether we could have gone further in that direction). Pierre Del Moral presented a broad overview of the Feynman-Kacs’ approaches to particle methods, in particular particle MCMC, with application to some financial objects. Paul Glasserman talked about robust MCMC, which I found quite an appealing concept in that it included uncertainties about the model itself. And linked with minimax concepts. And Paul Dupuis exposed a parallel tempering method linked with large deviations, whose paper I am definitely looking forward. Now it is more than time to work on my own talk! (On a very personal basis, I sadly lost my sturdy Canon camera in the taxi from the airport! Will need a new one for the ‘Og!)

workshop in Columbia

Posted in Statistics, Travel, University life with tags , , , on July 26, 2011 by xi'an

In late September, I will take part in a workshop in Columbia University on computational methods, which sounds quite exciting when judging from the above collection of speakers! (All interested readers should note that the workshop is free, but registration is compulsory. I will, of course!, be speaking about ABC methods.) Plus, it is always a particular treat to be back in New York City