Vivek Roy, Aixian Tan and James Flegal arXived a new paper, Estimating standard errors for importance sampling estimators with multiple Markov chains, where they obtain a central limit theorem and hence standard error estimates when using several MCMC chains to simulate from a mixture distribution as an importance sampling function. Just before I boarded my plane from Amsterdam to Calgary, which gave me the opportunity to read it completely (along with half a dozen other papers, since it is a long flight!) I first thought it was connecting to our AMIS algorithm (on which convergence Vivek spent a few frustrating weeks when he visited me at the end of his PhD), because of the mixture structure. This is actually altogether different, in that a mixture is made of unnormalised complex enough densities, to act as an importance sampler, and that, due to this complexity, the components can only be simulated via separate MCMC algorithms. Behind this characterisation lurks the challenging problem of estimating multiple normalising constants. The paper adopts the resolution by reverse logistic regression advocated in Charlie Geyer’s famous 1994 unpublished technical report. Beside the technical difficulties in establishing a CLT in this convoluted setup, the notion of mixing importance sampling and different Markov chains is quite appealing, especially in the domain of “tall” data and of splitting the likelihood in several or even many bits, since the mixture contains most of the information provided by the true posterior and can be corrected by an importance sampling step. In this very setting, I also think more adaptive schemes could be found to determine (estimate?!) the optimal weights of the mixture components.
Archive for Ames
Another busy day as I visited the University of Chicago Booth School of Business. This was my first time visit to this impressive building (and my first visit to Chicago for 25 years…) I actually had to leave Ames at 4:30 (am!) to catch a plane in Des Moines at 6:50 and be at the Chicago Booth before my first appointment at 10… Everything worked out fine, despite the potential for disruption due to the storm Sandy (just spotted a few big waves along the waterfront on my way to the University), and I had a definitely productive sequence of discussions. The talk on ABC was again well-attended and, because this was an econometric seminar (as in Princeton), definitely lively with a flow of questions all along. (There were also a few people from Biology, for whom the focus on our consistency result was presumably less interesting than for econometricians.) As in Ames, I did not manage to reach the part on empirical likelihood. Fodder for another seminar! The day ended by a meal in a superb restaurant with my favourite wine, Saint-Joseph, after which I was ready for a few hours of sleep..! And then a few hours to spend in the Art Institute of Chicago before flying back to Paris. Direct, courtesy of Sandy.
A short visit to ISU but and therefore a busy and proftable day! About ten appointments in Snedecor Hall after a nice morning run, a highly attended Zyskind Lecture, and many interesting discussions all over the day: e.g., I had a great time discussing using null recurrent Markov chains for integral approximations with Krishna Athreya and Vivek Roy, following Vivek’s seminar last week, ABC for spatial point processes with Alicia Carriquiry and Kristian Schmidt, SMC and ABC with [fellow blogger] Jarad Niemi, empirical likelihood with Song Chen, and hierarchical Bayes modelling and model checking with Mark Kaiser. I also met an impressive PhD student, Yihui Xie, who seems to have an endless pool of energy as he develops R packages by the dozen, such as animation, formatR, and knitr such as animation, formatR, and knitr, the later being an alternative to sweave, works on a book and seems to be contributing a lot to community sites like RPubs, in addition to maintaining his own blog… I actually took the opportunity to ask him a problem that bugged me for a while, namely how to include R code within beamer so that when I give a class/talk I can click on the code and see the output coming on the slide…
Next week, I will visit both Iowa State University, in Ames—a funny item for French speaking readers is that I will first land in Des Moines before reaching (les) Ames!, a logical step if any, even though only the first name relates to the early French exploration of the area: Ames has apparently no [ethymological] connection with souls…—, and the University of Chicago Booth Business School, giving a seminar on ABC model choice and empirical likelihood in both places. (I have never been to Iowa before and the last time I visited Chicago—rather than just commuting through O’Hare—was in May 1988, when I drove a friend to the airport…!) Here are the time and places for the seminars (note that the seminar at Booth is on Tuesday rather than on the customary Thursday to accommodate my tight schedule!):
- Monday Oct 29th, 4:10 pm, Snedecor 3105, Iowa State University, Zyskind lecture [abstract]
- Tuesday Oct 30th, 12:00pm, Lunch: C50B and 1:20pm Seminar: C50A, the University of Chicago Booth Business School, Econometrics and Statistics Colloquium [abstract]
As a coincidence—not so much as he is currently assistant professor in Ames—, the previous seminar speaker in Ames is my friend Vivek Roy, talking on Monte Carlo Methods for Improper Target Distributions! Here is (again!) the current version of the slides: