Van Dantzig Seminar

nationwide series of lectures in statistics

Home      David van Dantzig      About the seminar      Upcoming seminars      Previous seminars      Slides      Contact    

Van Dantzig Seminar: 28 February 2014

Programme: (click names or scroll down for titles and abstracts)

14:00 - 14:05 Opening
14:05 - 15:05 Andrew Gelman (Columbia University, New York)
15:05 - 15:25 Break
15:25 - 16:25 Harrison Zhou (Yale University)
16:30 - 17:30 Reception
Location: University of Amsterdam, Science Park, Room C1.110 (Directions)

Titles and abstracts

  • Andrew Gelman

    Choices is statistical graphics

    Graphics are a central part of statistical graphics but are typically neglected in statistical theory. We view graphics as a form of model checking, with interesting and surprising visual patterns corresponding to aspects of the data that are unexpected, that is were not likely to occur given the assumed model (which might be implicit). At the same time, graphics are an increasingly prevalent part of journalism. "Infographics" often have the goal of aesthetic appeal to draw a casual viewer in deeper, while "statistical graphics" often have the goal to reveal patterns for viewers who are already interested in the problem. We discuss all of these points in the context of graphics we have published for our research over the years.

    Download the slides (a previous version of the slides presented at the seminar)

  • Harrison Zhou

    Asymptotic Normality and Optimalities in Estimation of Large Gaussian Graphical Model

    The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This talk considers a fundamental question: When is it possible to estimate low-dimensional parameters at parametric square-root rate in a large Gaussian graphical model? A novel regression approach is proposed to obtain asymptotically efficient estimation of each entry of a precision matrix under a sparseness condition relative to the sample size. When the precision matrix is not sufficiently sparse, or equivalently the sample size is not sufficiently large, a lower bound is established to show that it is no longer possible to achieve the parametric rate in the estimation of each entry. This lower bound result, which provides an answer to the delicate sample size question, is established with a novel construction of a subset of sparse precision matrices in an application of Le Cam's Lemma. Moreover, the proposed estimator is proven to have optimal convergence rate when the parametric rate cannot be achieved, under a minimal sample requirement.

    The proposed estimator is applied to test the presence of an edge in the Gaussian graphical model or to recover the support of the entire model, to obtain adaptive rate-optimal estimation of the entire precision matrix as measured by the matrix lq operator norm, and to make inference in latent variables in the graphical model. All these are achieved under a sparsity condition on the precision matrix and a side condition on the range of its spectrum. This significantly relaxes the commonly imposed uniform signal strength condition on the precision matrix, irrepresentable condition on the Hessian tensor operator of the covariance matrix or the l1 constraint on the precision matrix. Numerical results confirm our theoretical findings. The ROC curve of the proposed algorithm, Asymptotic Normal Thresholding (ANT), for support recovery significantly outperforms that of the popular GLasso algorithm.

    Download the slides

Supported by

BTK, Amsterdam 2014