The afternoon on model choice at the London School of Hygiene (!) and Tropical Medicine was worth the short trip from Paris, especially when the weather in London felt like real summer: walking in the streets was a real treat! The talks were also interesting in that the emphasis was off-key from my usual statistics talks and thus required more focus from me. The first talk by Stijn Vansteelandt emphasized (very nicely) the role of confounders and exposure in causal inference in ways that were novel to me (although it seems in the end that a proper graphical modelling of all quantities involved in the process would allow for a standard statistical analysis). I also had troubles envisioning the Bayesian version of the approach, although Stijn referred to a recent paper by Wang et al. While Stijn has a joint paper in the Series B that just arrived on my desk, this talk is more related to appear in Statistical Methodology in Medical Research (The second talk was mine and presumably too technical in that I should have gotten rid of the new mathematical assumptions [A1]-[A4] altogether.) The third was a fascinating statistical analysis by Doug Speed of an important genetic heritability paper, by Yang et al., where he took the assumptions of the model one at a time to see how they were impacting the conclusions and found that none was to blame. The fourth and final talk by David Clayton covered the role of link functions in GLMs applied to epidemiological models, in connection with older papers from the 1990′s, to conclude that the choice of the link function mattered for the statistical properties of the variable selection procedures, which I found a bit puzzling based on my (limited) econometric intuition that all link functions lead to consistent pseudo-models. In any case, this was a fairly valuable meeting, furthermore attended by a very large audience.
Archive for March, 2012
What are the distributions on the positive k-dimensional quadrant with parametrizable covariance matrix?Posted in Books, pictures, Statistics, University life with tags correlation, covariance, covariance matrix, linear algebra, matrix algebra, multivariate analysis, positive quadrant on March 30, 2012 by xi'an
Y = μ + Σ X
could lead to negative components in Y…. After searching a little while, I could not think of a joint distribution on the positive k-dimensional quadrant where I could specify the covariance matrix in advance. Except for a pedestrian construction of (x1,x2) where x1 would be an arbitrary Gamma variate [with a given variance] and x2 conditional on x1 would be a Gamma variate with parameters specified by the covariance matrix. Which does not extend nicely to larger dimensions.
On Tuesday and Wednesday, next week, I will give seminars in Princeton University and Rutgers University, respectively. My talk at Princeton actually takes place in the Department of Economics, at the Oskar Morgenstern Memorial Seminar (Tuesday, April 3, 2:40 – 4:00pm 200 Fisher Hall). I must acknowledge that the prospect is a wee daunting. For addressing the manes of Morgenstern and for speaking in Nash‘s very own institution, if nothing else! And my talk at Rutgers is in the Department of Statistics and Bostatistics (Wedn, April 4, 3:20 – 4:20, Hill Center, Busch Campus), where I will meet with my friend of many years Bill Strawderman. And my former PhD student Aude Grelaud. Both talks will cover the same ground of ABC model choice and Bayesian consistency (surprise, surprise!). The format of the econometrics seminar at Princeton being a bit longer, I will give more background on ABC, mostly in connection with the econometric methods I mentioned in my ABC tutorial in Roma and at CREST. I presume I will skip this part in Rutgers as biologists and geneticists are more likely to attend than econometricians. In preparation, here is the current version of the talk, to be updated till Monday at the very least!
Statistical Science just ran a special issue (Feb. 2012) as a tribute to Charles Stein that focused on shrinkage estimation. Shrinkage and the Stein effect have been my entries to the Bayesian (wonderful) world, so I read through this series of papers edited by Ed George and Bill Strawderman with fond remembrance. The more because most of the authors are good friends! Jim Berger, Bill Jefferys, and Peter Müller consider shrinkage estimation for wavelet coefficients and applies it to Cepheid variable stars. The paper by Ann Brandwein and Bill Strawderman is a survey of shrinkage estimation and the Stein effect for spherically elliptical distributions, precisely my PhD thesis topic and main result! Larry Brown and Linda Shao give a geometric interpretation of the original Stein (1956) paper. Tony Cai discusses the concepts of minimaxity and shrinkage estimators in functional spaces. George Casella and Juinn Gene Hwang recall the impact of shrinkage estimation on confidence sets. Dominique Fourdrinier and Marty Wells give an expository development of loss estimation using shrinkage estimators. Ed George, Feng Liang and Xinyi Xu recall how shrinkage estimation was recently extended to prediction using Kullback-Leibler losses. Carl Morris and Martin Lysy detail the reversed shrinkage defect and Model-II minimaxity in the normal case. Gauri Datta and Malay Ghosh explain how shrinkage estimators are paramount in small area estimation, providing a synthesis between both the Bayesian and the frequentist points of view. At last, Michael Perlman and Sanjay Chaudhuri reflect on the reversed shrinkage effect, providing us with several pages of Star Trek dialogues on this issue, and more seriously voicing a valid Bayesian reservation!