/post/index.xml Past Seminar Series - McGill Statistics Seminars

Past Seminar Series

  • Divergence based inference for general estimating equations

    Anand N. Vidyashankar · Feb 14, 2014

    Date: 2014-02-14

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Hellinger distance and its variants have long been used in the theory of robust statistics to develop inferential tools that are more robust than the maximum likelihood but as ecient as the MLE when the posited model holds. A key aspect of this alternative approach requires speci cation of a parametric family, which is usually not feasible in the context of problems involving complex data structures wherein estimating equations are typically used for inference. In this presentation, we describe how to extend the scope of divergence theory for inferential problems involving estimating equations and describe useful algorithms for their computation. Additionally, we theoretically study the robustness properties of the methods and establish the semi-parametric eciency of the new divergence based estimators under suitable technical conditions. Finally, we use the proposed methods to develop robust sure screening methods for ultra high dimensional problems. Theory of large deviations, convexity theory, and concentration inequalities play an essential role in the theoretical analysis and numerical development. Applications from equine parasitology, stochastic optimization, and antimicrobial resistance will be used to describe various aspects of the proposed methods.

  • Statistical techniques for the normalization and segmentation of structural MRI

    Taki Shinohara · Feb 7, 2014

    Date: 2014-02-07

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    While computed tomography and other imaging techniques are measured in absolute units with physical meaning, magnetic resonance images are expressed in arbitrary units that are difficult to interpret and differ between study visits and subjects. Much work in the image processing literature has centered on histogram matching and other histogram mapping techniques, but little focus has been on normalizing images to have biologically interpretable units. We explore this key goal for statistical analysis and the impact of normalization on cross-sectional and longitudinal segmentation of pathology.

  • An exchangeable Kendall's tau for clustered data

    Hela Romdhani · Jan 31, 2014

    Date: 2014-01-31

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    I’ll introduce the exchangeable Kendall’s tau as a nonparametric intra class association measure in a clustered data frame and provide an estimator for this measure. The asymptotic properties of this estimator are investigated under a multivariate exchangeable cdf. Two applications of the proposed statistic are considered. The first is an estimator of the intraclass correlation coefficient for data drawn from an elliptical distribution. The second is a semi-parametric intraclass independence test based on the exchangeable Kendall’s tau.

  • Calibration of computer experiments with large data structures

    Derek Bingham · Jan 24, 2014

    Date: 2014-01-24

    Time: 15:30-16:30

    Location: Salle 1355, pavillon André-Aisenstadt (CRM)

    Abstract:

    Statistical model calibration of computer models is commonly done in a wide variety of scientific endeavours. In the end, this exercise amounts to solving an inverse problem and a form of regression. Gaussian process model are very convenient in this setting as non-parametric regression estimators and provide sensible inference properties. However, when the data structures are large, fitting the model becomes difficult. In this work, new methodology for calibrating large computer experiments is presented. We proposed to perform the calibration exercise by modularizing a hierarchical statistical model with approximate emulation via local Gaussian processes. The approach is motivated by an application to radiative shock hydrodynamics.

  • An introduction to stochastic partial differential equations and intermittency

    Raluca Balan · Jan 10, 2014

    Date: 2014-01-10

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    In a seminal article in 1944, Itô introduced the stochastic integral with respect to the Brownian motion, which turned out to be one of the most fruitful ideas in mathematics in the 20th century. This lead to the development of stochastic analysis, a field which includes the study of stochastic partial differential equations (SPDEs). One of the approaches for the study of SPDEs was initiated by Walsh (1986) and relies on the concept of random-field solution for equations perturbed by a space-time white noise (or Brownian sheet). This concept allows us to investigate the dynamical changes in the probabilistic behavior of the solution, simultaneously in time and space. These developments will be reviewed in the first part of the talk. The second part of the talk will be dedicated to some recent advances in this area, related to the existence of a random-field solution for some classical SPDEs (like the stochastic heat equation) perturbed by a colored'' noise, which behaves in time like the fractional Brownian motion. When this solution exists, it exhibits a strong form of intermittency,’’ a property which was originally introduced in the physics literature for describing random fields whose values develop very large peaks. This talk is based on some recent joint work with Daniel Conus (Lehigh University).

  • Great probabilists publish posthumously

    Stephen M. Stigler · Dec 6, 2013

    Date: 2013-12-06

    Time: 15:30-16:30

    Location: UQAM Salle SH-3420

    Abstract:

    Jacob Bernoulli died in 1705. His great book Ars Conjectandi was published in 1713, 300 years ago. Thomas Bayes died in 1761. His great paper was read to the Royal Society of London in December 1763, 250 years ago, and published in 1764. These anniversaries are noted by discussing new evidence regarding the circumstances of publication, which in turn can lead to a better understanding of the works themselves. As to whether or not these examples of posthumous publication suggest a career move for any modern probabilist; that question is left to the audience.

  • Signal detection in high dimension: Testing sphericity against spiked alternatives

    Marc Hallin · Nov 29, 2013

    Date: 2013-11-29

    Time: 15:30-16:30

    Location: Concordia MB-2.270

    Abstract:

    We consider the problem of testing the null hypothesis of sphericity for a high-dimensional covariance matrix against the alternative of a finite (unspecified) number of symmetry-breaking directions (multispiked alternatives) from the point of view of the asymptotic theory of statistical experiments. The region lying below the so-called phase transition or impossibility threshold is shown to be a contiguity region. Simple analytical expressions are derived for the asymptotic power envelope and the asymptotic powers of existing tests. These asymptotic powers are shown to lie very substantially below the power envelope; some of them even trivially coincide with the size of the test. In contrast, the asymptotic power of the likelihood ratio test is shown to be uniformly close to the same.

  • Tail order and its applications

    Lei Hua · Nov 22, 2013

    Date: 2013-11-22

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Tail order is a notion for quantifying the strength of dependence in the tail of a joint distribution. It can account for a wide range of dependence, ranging from tail positive dependence to tail negative dependence. We will introduce theory and applications of tail order. Conditions for tail orders of copula families will be discussed, and they are helpful in guiding us to find suitable copula families for statistical inference. As applications of tail order, regression analysis will be demonstrated, using appropriately constructed copulas, that can capture the unique tail dependence patterns appear in a medical expenditure panel survey data.

  • Submodel selection and post estimation: Making sense or folly

    Syed Ejaz Ahmed · Nov 15, 2013

    Date: 2013-11-15

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    In this talk, we consider estimation in generalized linear models when there are many potential predictors and some of them may not have influence on the response of interest. In the context of two competing models where one model includes all predictors and the other restricts variable coefficients to a candidate linear subspace based on subject matter or prior knowledge, we investigate the relative performances of Stein type shrinkage, pretest, and penalty estimators (L1GLM, adaptive L1GLM, and SCAD) with respect to the full model estimator. The asymptotic properties of the pretest and shrinkage estimators including the derivation of asymptotic distributional biases and risks are established. A Monte Carlo simulation study show that the mean squared error (MSE) of an adaptive shrinkage estimator is comparable to the MSE of the penalty estimators in many situations and in particular performs better than the penalty estimators when the model is sparse. A real data set analysis is also presented to compare the suggested methods.

  • The inadequacy of the summed score (and how you can fix it!)

    Daphna Harel · Nov 8, 2013

    Date: 2013-11-08

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Health researchers often use patient and physician questionnaires to assess certain aspects of health status. Item Response Theory (IRT) provides a set of tools for examining the properties of the instrument and for estimation of the latent trait for each individual. In my research, I critically examine the usefulness of the summed score over items and an alternative weighted summed score (using weights computed from the IRT model) as an alternative to both the empirical Bayes estimator and maximum likelihood estimator for the Generalized Partial Credit Model. First, I will talk about two useful theoretical properties of the weighted summed score that I have proven as part of my work. Then I will relate the weighted summed score to other commonly used estimators of the latent trait. I will demonstrate the importance of these results in the context of both simulated and real data on the Center for Epidemiological Studies Depression Scale.