Yesterday, I (we) found myself (ourselves) back in time, precisely 34 years ago, as we drove our daughter to Orly airport for her flight to Cayenne, French Guiana. And the start of her internship. Indeed, this is also the airport from which I left for Purdue University in 1987 and where my parents drove me then, more for sentimental reasons than out of necessity, as I had much less luggage than Rachel! This old airport has not changed that much, apart from the sharp increase in security restrictions. At the time, my parents were able to stay till the plane to Chicago left (two hours late) and watch it take off from the terraces of the airport. This time, we were just unable to enter the airport beyond the parking lot and watched the plane take off (one hour late) from a flight tracker! But overall there was the same bittersweet feeling of seeing one’s kid move (far) away for a major and exciting step in their professional life. (When I called my mom to watch for the plane flying west straight across Normandy, very close to our family roots, she reminded me of that and also of my grand-parents watching my plane flying by… Without a flight tracker! I actually remember spotting Mont Saint-Michel on that trip.) Fare well, Dr. R, and see you soon!
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Archive for Purdue University
three decades back
Posted in Kids, Travel with tags airport, Alicia Dickenstein, Cayenne, Chicago, flight, Guiana, Guyane, Mont-Saint-Michel, Orly, Purdue University on October 25, 2021 by xi'anestimation of a normal mean matrix
Posted in Statistics with tags Biometrika, Charles Stein, Cornell University, James-Stein estimator, Purdue University, Rutgers University, shrinkage estimation, Springer-Verlag, superharmonicity, Université de Rouen on May 13, 2021 by xi'an
A few days ago, I noticed the paper Estimation under matrix quadratic loss and matrix superharmonicity by Takeru Matsuda and my friend Bill Strawderman had appeared in Biometrika. (Disclaimer: I was not involved in handling the submission!) This is a “classical” shrinkage estimation problem in that covariance matrix estimators are compared under under a quadratic loss, using Charles Stein’s technique of unbiased estimation of the risk is derived. The authors show that the Efron–Morris estimator is minimax. They also introduce superharmonicity for matrix-variate functions towards showing that generalized Bayes estimator with respect to a matrix superharmonic priors are minimax., including a generalization of Stein’s prior. Superharmonicity that relates to (much) earlier results by Ed George (1986), Mary-Ellen Bock (1988), Dominique Fourdrinier, Bill Strawderman, and Marty Wells (1998). (All of whom I worked with in the 1980’s and 1990’s! in Rouen, Purdue, and Cornell). This paper also made me realise Dominique, Bill, and Marty had published a Springer book on Shrinkage estimators a few years ago and that I had missed it..!
the buzz about nuzz
Posted in Books, Mountains, pictures, Statistics with tags Hamiltonian Monte Carlo, HMC, Jim Berger, Loch Lomond, MALA, Metropolis-Hastings algorithm, partly deterministic processes, PDMP, Poisson process, Purdue University, root finding, Tom Sellke, Wasserstein distance, Zig-Zag on April 6, 2020 by xi'an
“…expensive in these terms, as for each root, Λ(x(s),v) (at the cost of one epoch) has to be evaluated for each root finding iteration, for each node of the numerical integral“
When using the ZigZag sampler, the main (?) difficulty is in producing velocity switch as the switches are produced as interarrival times of an inhomogeneous Poisson process. When the rate of this process cannot be integrated out in an analytical manner, the only generic approach I know is in using Poisson thinning, obtained by finding an integrable upper bound on this rate, generating from this new process and subsampling. Finding the bound is however far from straightforward and may anyway result in an inefficient sampler. This new paper by Simon Cotter, Thomas House and Filippo Pagani makes several proposals to simplify this simulation, Nuzz standing for numerical ZigZag. Even better (!), their approach is based on what they call the Sellke construction, with Tom Sellke being a probabilist and statistician at Purdue University (trivia: whom I met when spending a postdoctoral year there in 1987-1988) who also wrote a fundamental paper on the opposition between Bayes factors and p-values with Jim Berger.
“We chose as a measure of algorithm performance the largest Kolmogorov-Smirnov (KS) distance between the MCMC sample and true distribution amongst all the marginal distributions.”
The practical trick is rather straightforward in that it sums up as the exponentiation of the inverse cdf method, completed with a numerical resolution of the inversion. Based on the QAGS (Quadrature Adaptive Gauss-Kronrod Singularities) integration routine. In order to save time Kingman’s superposition trick only requires one inversion rather than d, the dimension of the variable of interest. This nuzzled version of ZIgZag can furthermore be interpreted as a PDMP per se. Except that it retains a numerical error, whose impact on convergence is analysed in the paper. In terms of Wasserstein distance between the invariant measures. The paper concludes with a numerical comparison between Nuzz and random walk Metropolis-Hastings, HMC, and manifold MALA, using the number of evaluations of the likelihood as a measure of time requirement. Tuning for Nuzz is described, but not for the competition. Rather dramatically the Nuzz algorithm performs worse than this competition when counting one epoch for each likelihood computation and better when counting one epoch for each integral inversion. Which amounts to perfect inversion, unsurprisingly. As a final remark, all models are more or less Normal, with very smooth level sets, maybe not an ideal range
Rao-Blackwellisation, a review in the making
Posted in Statistics with tags Andrei Kolmogorov, birthday, C.R. Rao, computational statistics, David Blackwell, Monte Carlo methods, Purdue University, Rao-Blackwell theorem, Rao-Blackwellisation, review, survey on March 17, 2020 by xi'an
Recently, I have been contacted by a mainstream statistics journal to write a review of Rao-Blackwellisation techniques in computational statistics, in connection with an issue celebrating C.R. Rao’s 100th birthday. As many many techniques can be interpreted as weak forms of Rao-Blackwellisation, as e.g. all auxiliary variable approaches, I am clearly facing an abundance of riches and would thus welcome suggestions from Og’s readers on the major advances in Monte Carlo methods that can be connected with the Rao-Blackwell-Kolmogorov theorem. (On the personal and anecdotal side, I only met C.R. Rao once, in 1988, when he came for a seminar at Purdue University where I was spending the year.)
patterned random matrices [not a book review]
Posted in Books, pictures, Statistics, University life with tags Arup Bose, book review, Indian Statistical Institute, Kolkata, Purdue University, random matrices on October 24, 2018 by xi'an
