Archive for Basu’s theorem

exams

Posted in Kids, Statistics, University life with tags , , , , , , , on February 7, 2018 by xi'an
As in every term, here comes the painful week of grading hundreds of exams! My mathematical statistics exam was highly traditional and did not even involve Bayesian material, as the few students who attended the lectures were so eager to discuss sufficiency and ancilarity, that I decided to spend an extra lecture on these notions rather than rushing though conjugate priors. Highly traditional indeed with an inverse Gaussian model and a few basic consequences of Basu’s theorem. actually exposed during this lecture. Plus mostly standard multiple choices about maximum likelihood estimation and R programming… Among the major trends this year, I spotted out the widespread use of strange derivatives of negative powers, the simultaneous derivation of two incompatible convergent estimates, the common mixup between the inverse of a sum and the sum of the inverses, the inability to produce the MLE of a constant transform of the parameter, the choice of estimators depending on the parameter, and a lack of concern for Fisher informations equal to zero.

parallel Metropolis Hastings [published]

Posted in Statistics, University life with tags , , , , on October 27, 2011 by xi'an

As I was looking at the discussion paper by Yamin Yu and Xiao-Li Meng on improved efficiency for MCMC algorithms, which is available (for free) on-line, I realised the paper on parallel Metropolis-Hastings algorithm we wrote with Pierre Jacob and Murray Smith is now published in Journal of Computational and Graphical Statistics (on-line). This is a special issue for the 20th anniversary of the Journal of Computational and Graphical Statistics and our paper is within the “If Monte Carlo Be a Food of Computing, Simulate on” section! (My friends Olivier Cappé and Radu V. Craiu also have a paper in this issue.)  Here is the complete reference:

P. Jacob, C. P. Robert, & M. H. Smith. Using Parallel Computation to Improve Independent Metropolis–Hastings Based Estimation. Journal of Computational and Graphical Statistics. September 1, 2011, 20(3): 616-635. doi:10.1198/jcgs.2011.10167

The [20th Anniversary Featured Discussion] paper by Yamin Yu and Xiao-Li Meng has already been mentioned on Andrew’s blog, it is full of interesting ideas and remarks about improving Gibbs efficiency, in the spirit of the very fine work Jim Hobert and his collaborators have been developing in the past decade,  fun titles (“To center or not center – that is not the question”, “coupling is more promising than compromising”, “be all our insomnia remembered”, and “needing inception”, in connection with the talk Xiao-Li gave in Paris two months ago….), and above all the fascinating puzzle of linking statistical concepts and Monte Carlo concepts. How comes sufficiency and ancillarity are to play a role in simulation?! Where is the simulation equivalent of Basu’s theorem? These questions obviously relate to the idea of turning simulation into a measure estimation issue, discussed in a post of mine after the Columbia workshop. This interweaving paper also brings back memories of the fantastic Biometrika 1994 interleaving paper by Liu, Wong, and Kong, with its elegant proof of positive decreasing correlation and of improvement by Rao-Blackwellisation [another statistics theorem!] for data augmentation.