/tags/2014-winter/index.xml 2014 Winter - McGill Statistics Seminars

2014 Winter

  • Adaptive piecewise polynomial estimation via trend filtering

    Ryan Tibshirani · Apr 11, 2014

    Date: 2014-04-11

    Time: 15:30-16:30

    Location: Salle KPMG, 1er étage HEC Montréal

    Abstract:

    We will discuss trend filtering, a recently proposed tool of Kim et al. (2009) for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the penalty term sums the absolute kth order discrete derivatives over the input points. Perhaps not surprisingly, trend filtering estimates appear to have the structure of kth degree spline functions, with adaptively chosen knot points (we say “appear” here as trend filtering estimates are not really functions over continuous domains, and are only defined over the discrete set of inputs). This brings to mind comparisons to other nonparametric regression tools that also produce adaptive splines; in particular, we will compare trend filtering to smoothing splines, which penalize the sum of squared derivatives across input points, and to locally adaptive regression splines (Mammen & van de Geer 1997), which penalize the total variation of the kth derivative.

  • Some aspects of data analysis under confidentiality protection

    Bimal Sinha · Apr 4, 2014

    Date: 2014-04-04

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Statisticians working in most federal agencies are often faced with two conflicting objectives: (1) collect and publish useful datasets for designing public policies and building scientific theories, and (2) protect confidentiality of data respondents which is essential to uphold public trust, leading to better response rates and data accuracy. In this talk I will provide a survey of two statistical methods currently used at the U.S. Census Bureau: synthetic data and noise perturbed data.

  • 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.

  • Insurance company operations and dependence modeling

    Jed Frees · Mar 21, 2014

    Date: 2014-03-21

    Time: 15:30-16:30

    Location: BURN 107

    Abstract:

    Actuaries and other analysts have long had the responsibility in insurance company operations for various financial functions including (i) ratemaking, the process of setting premiums, (ii) loss reserving, the process of predicting obligations that arise from policies, and (iii) claims management, including fraud detection. With the advent of modern computing capabilities and detailed and novel data sources, new opportunities to make an impact on insurance company operations are extensive.

  • 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.

  • ABC as the new empirical Bayes approach?

    Christian Robert · Feb 28, 2014

    Date: 2014-02-28

    Time: 13:30-14:30

    Location: UdM, Pav. Roger-Gaudry, Salle S-116

    Abstract:

    Approximate Bayesian computation (ABC) has now become an essential tool for the analysis of complex stochastic models when the likelihood function is unavailable. The approximation is seen as a nuisance from a computational statistic point of view but we argue here it is also a blessing from an inferential perspective. We illustrate this paradoxical stand in the case of dynamic models and population genetics models. There are also major inference difficulties, as detailed in the case of Bayesian model choice.

  • 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.