/categories/mcgill-statistics-seminar/index.xml McGill Statistics Seminar - McGill Statistics Seminars

McGill Statistics Seminar

  • How much does the dependence structure matter?

    Ruodu Wang · Mar 28, 2014

    Date: 2014-03-28

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    In this talk, we will look at some classical problems from an anti-traditional perspective. We will consider two problems regarding a sequence of random variables with a given common marginal distribution. First, we will introduce the notion of extreme negative dependence (END), a new benchmark for negative dependence, which is comparable to comonotonicity and independence. Second, we will study the compatibility of the marginal distribution and the limiting distribution when the dependence structure in the sequence is allowed to vary among all possibilities. The results are somewhat simple, yet surprising. We will provide some interpretation and applications of the theoretical results in financial risk management, with the hope to deliver the following message: with the common marginal distribution known and dependence structure unknown, we know essentially nothing about the asymptotic shape of the sum of random variables.

  • Mixed effects trees and forests for clustered data

    Denis Larocque · Mar 14, 2014

    Date: 2014-03-14

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    In this talk, I will present extensions of tree-based and random forest methods for the case of clustered data. The proposed methods can handle unbalanced clusters, allows observations within clusters to be splitted, and can incorporate random effects and observation-level covariates. The basic tree-building algorithm for a continuous outcome is implemented using standard algorithms within the framework of the EM algorithm. The extension to other types of outcomes (e.g., binary, count) uses the penalized quasi-likelihood (PQL) method for the estimation and the EM algorithm for the computation. Simulation results show that the proposed methods provides substantial improvements over standard trees and forests when the random effects are non negligible. The use of the method will be illustrated with real data sets.

  • On the multivariate analysis of neural spike trains: Skellam process with resetting and its applications

    Reza Ramezan · Feb 21, 2014

    Date: 2014-02-21

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Nerve cells (a.k.a. neurons) communicate via electrochemical waves (action potentials), which are usually called spikes as they are very localized in time. A sequence of consecutive spikes from one neuron is called a spike train. The exact mechanism of information coding in spike trains is still an open problem; however, one popular approach is to model spikes as realizations of an inhomogeneous Poisson process. In this talk, the limitations of the Poisson model are highlighted , and the Skellam Process with Resetting (SPR) is introduced as an alternative model for the analysis of neural spike trains. SPR is biologically justified, and the parameter estimation algorithm developed for it is computationally efficient. To allow for the modelling of neural ensembles, this process is generalized to the multivariate case, where Multivariate Skellam Process with Resetting (MSPR), as well as the multivariate Skellam distribution are introduced. Simulation and real data studies confirm the promising results of the Skellam model in the statistical analysis of neural spike trains.

  • 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.

  • 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).

  • 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.