Seminar Dates, Speakers & Title Details 2008
Speaker: David Stanford
University of Western Ontario
Title: A common phase-type structure for a large class of perturbed risk processes
Abstract: Recently there has been substantial interest in identifying suitable structures for the ruin probability for perturbed risk models. Among these, several papers have identified a phase-type structure for specific cases of these perturbed risk models. At the same time, a phase type structure had already been identified by Asmussen in 1995 for stationary probabilities for a class of perturbed fluid-flow models, who also related this to certain transient probabilities. In the present talk, we illustrate just how large the class of perturbed risk models is that can be handled by Asmussen's fluid flow approach, and identify the standard template that can be followed to compute the ultimate ruin probability for all such models, as well as identifying the its components due to claims and due to diffusion. If time permits, the extension of this method via Erlangization for time-varying ruin probabilities will be discussed.
This talk is based on joint work with Jiandong Ren and Kaiqi Yu of UWO, and Lothar Breuer of the Unviersity of Kent, UK.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5158
Speaker: Ayesha Ali
University of Guelph
Title: Representing Equivalence Classes of Directed Acyclic Graphs in the Presence of Latent Variables
Abstract: Graphical models are graphs with vertices (variables) and edges that encode the conditional independence relations holding among the set of variables of some process. Directed acyclic graphs (DAGs) are commonly used to represent processes in (not exclusively) the biological, econometric, and social sciences. However, there are often many graphs that can encode the same set of conditional independence relations, thus forming a Markov equivalence class. Furthermore, the likelihoods of Markov equivalent graphs are equal. Hence, when performing a model search, it may be more efficient to search across equivalence classes rather than across individual graphs.
In this talk we will review how equivalence classes of DAG models are represented. We will then focus on situations where some of the variables in the process are latent, and discuss how to represent Markov equivalence classes in this setting.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5158
Speaker: Geoff Fong, Mary Thompson, others in the UW ITC team
Department of Psychology
Title: Using the ITC data sets
Abstract: The International Tobacco Control Policy Evaluation Project (ITC Project) carries out nationally representative longitudinal surveys of smokers in several countries around the world. The purpose of this seminar is to let members of the department know about the possibilities of the data sets for research in longitudinal data analysis and survey methods. The seminar will begin with a brief introduction to the ITC surveys, followed by an outline of the data sets so far collected and processed, and some of the methodological questions of interest to the investigators. The data sharing policy will be described, including restrictions and conditions on access, and the procedures for obtaining access. This will be followed by a question and answer period.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5158
Speaker: Andrei Badescu University of Toronto
University of Toronto
Title: Return Probabilities of Stochastic Fluid Flows and Their Use in Collective
Risk Theory
Abstract: One way of analyzing insurance risk models is by making use of the existing connections with stochastic fluid flows. Matrix-analytic methods constitute a useful approach to the study of such fluid flow models. In the present talk we illustrate the derivation of several first passage probabilities whose numerical calculation is very tractable, based on the structure and the probabilistic meaning of certain matrices describing these fluid models. In the end, we enumerate several classes of risk processes that can be analyzed using these probabilistic tools.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5158
Speaker: Geoffrey E. Hinton
Department of Computer Science, University of Toronto
and
Canadian Institute for Advanced Research
Title: THE NEXT GENERATION OF NEURAL NETWORKS
Abstract: In the 1980's, new learning algorithms for neural networks promised to solve difficult classification tasks, like speech or object recognition, by learning many layers of non-linear features. The results were mostly disappointing for two reasons: There was never enough labeled data to learn millions of complicated features and the learning was much too slow in deep neural networks with many layers of unconstrained features. These problems can now be overcome by learning one layer of features at a time and by changing the goal of learning. Instead of trying to predict the labels, the learning algorithm tries to create a multilayer generative model that produces data which looks just like the unlabeled training data. After learning many layers of features greedily, the whole network can be fine-tuned to give better discrimination by using the precious label information to slightly adjust the features discovered by the generative model. These deep neural networks outperform other machine learning methods, especially when labeled data is scarce but unlabeled data is plentiful.
Biography:
Geoffrey Hinton received his BA in experimental psychology from Cambridge in 1970 and his PhD in Artificial Intelligence from Edinburgh in 1978. He did postdoctoral work at Sussex University and the University of California San Diego and spent five years as a faculty member in the Computer Science department at Carnegie-Mellon University. He then moved to the Department of Computer Science at the University of Toronto. He spent three years from 1998 until 2001 setting up the Gatsby Computational Neuroscience Unit at University College London and then returned to the University of Toronto where he holds a Canada Research Chair in Machine Learning.
Dr. Hinton is a fellow of the Royal Society, the Royal Society of
Canada, and the American Association for Artificial Intelligence. He
is an honorary foreign member of the American Academy of Arts and
Sciences, and a former president of the Cognitive Science Society. He
received an honorary doctorate from the University of Edinburgh in 2001. He was awarded the first David E. Rumelhart prize (2001), the
IJCAI Award for Research Excellence (2005), the IEEE Neural Network
Pioneer award (1998) and the ITAC/NSERC award for contributions to
information technology (1992).
He was one of the researchers who introduced the back-propagation
algorithm that has been widely used for practical applications. His
other contributions include Boltzmann machines, distributed
representations, time-delay neural nets, mixtures of experts,
Helmholtz machines and products of experts.
Time: 2:00 pm.
Place: Davis Centre, Room DC1304
Speaker: Lang Wu
University of British Columbia
Title: Mixed Effects Models with Missing Data and Measurement Errors
Abstract: Mixed-effects or random-effects models are useful for analyzing longitudinal data or survival data. In mixed-effects models, correlation within clusters or repeated measurements are incorporated through random effects, which also allow individual-specific inference as well as population inference. Commonly used mixed models include linear mixed models, generalized linear mixed models, nonlinear mixed-effects models, and frailty models. Missing data and measurement errors are very common in longitudinal studies. We consider likelihood methods for mixed effects models with incompletely observed data, and consider EM algorithms and Taylor/Laplace approximations for estimation. We illustrate the methods using HIV viral dynamic models.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5158
Speaker:Bala Rajaratnam
Stanford University
Title: Flexible Covariance estimation in Gaussian Graphical models
Abstract: Covariance estimation is known to be a challenging problem, especially for high-dimensional data. In this context, graphical models can act as a tool for regularization and have proven to be excellent tools for the analysis of high dimensional data. Graphical models are statistical models where dependencies between variables are represented by means of a graph. Both frequentist and Bayesian inferential procedures for graphical models have recently received much attention in the statistics literature. The hyper-inverse Wishart distribution is a commonly used prior for Bayesian inference on covariance matrices in Gaussian Graphical models. This prior has the distinct advantage that it is a conjugate prior for this model but it suffers from lack of flexibility in high dimensional problems due to its single shape parameter.
In this talk, for posterior inference on covariance matrices in decomposable Gaussian graphical models, we use a flexible class of conjugate prior distributions defined on the cone of positive-definite matrices with fixed zeros according to a graph G. This class includes the hyper inverse Wishart distribution and allows for up to k+1 shape parameters where k denotes the number of cliques in the graph. We first add to this class of priors, a reference prior, which can be viewed as an improper member of this class. We then derive the general form of the Bayes estimators under traditional loss functions adapted to graphical models and exploit the conjugacy relationship in these models to express these estimators in closed form. The closed form solutions allow us to avoid heavy computational costs that are usually incurred in these high-dimensional problems. We also investigate decision-theoretic properties of the standard frequentist estimator, which is the maximum likelihood estimator, in these problems. Furthermore, we illustrate the performance of our estimators through numerical examples and comparisons with previous work where we explore frequentist risk properties and the efficacy of graphs in the estimation of high-dimensional covariance structures. We demonstrate that our estimators yield substantial risk reductions over the maximum likelihood estimator in the graphical model.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5158
Speaker: Michael Wolfson
Stats Canada
Title: On Complex Systems Theory and Population Health Should the Twain Meet?
Abstract: Two important and recent strands of intellectual development are complex systems theory, and population health. One important facet of complex systems theory is agent-based computer simulation models. These models offer important new possibilities for understanding a range of social phenomena, though current models are, by and large, highly abstract and sylized. At the same time, there has been strong growth in the field of population health (also called social epidemiology), for which a central premise is that the determinants of health are myriad, often complex, and include factors well beyond conventional health care – in particular aspects of the social environment. Important challenges in population health include the empirical and statistical question of how to elicit accurate descriptions of the main causal pathways. But equally important is means for representing, manipulating, and drawing out quantitative implications from coherent but at the same time diverse findings. This talk will explore the potential for agent-based simulation models to form the quantitative foundations for analysis in population health.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5158
Speaker: Russel Steele
McGill University
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5158
NOTE: NOT THE USUAL TIME OR DAY
Speaker: Hugh Chipman
Canada Research Chair in Mathematical Modelling, Acadia
University
Title: Statistical Learning from Complex Data
Abstract: These days, there's all kinds of weird and wonderful data out there.
The availability of such data, and the underlying scientific problems
represent a "field day" for inventors of new statistical methods. In
this talk, I'll outline several interesting areas, focusing on what
the challenges are, and how statistical ideas can play a crucial role
in addressing scientific questions. Specific areas discussed will
include social network modelling for mining transactional data on
networks (e.g. e-mail communications), techniques for clustering
curves that enable process monitoring, flexible supervised learning
methods that can be used for "active learning" (a.k.a. sequential
design), and methods tailored to enable the detection of "rare
targets" such as the next blockbuster drug.
This talk will be reasonably non-technical, and should be accessible to upper-year honours students or graduate students.
Time: 3:00 pm.
Place: Math & Computing Bldg, Room MC5158
Speaker: Radu Craiu
University of Toronto
Title: Learn from Thy Neighbour: Parallel-Chain Adaptive MCMC
Abstract: A considerable amount of effort has been recently invested in developing a comprehensive theory for adaptive MCMC. In comparison, there are fewer adaptive algorithms designed for practical situations.
I will review some of the theoretical approaches used for proving convergence of non-Markovian adaptation schemes and will discuss scenarios for which the original adaptive Random-Walk Metropolis is unsuitable.
Alternative adaptive schemes involving inter-chain and regional adaptation are discussed. Some of the proposed solutions involve theoretical questions that are still open.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5158
Speaker: Runhuan Feng
Department of Statistics and Actuarial Science
University of Waterloo
Title: Unlock Your Actuarial Fantasy - Stochastic Compound Interest Models
Abstract:Have you tired of hearing about short rate models in finance over and over again? Have you ever fantasized about interest rate models that are based on our knowledge of compound interest from the first course of theory of interest (ACTSC 231 @UW)? Would you want to know how an actuary can possibly evaluate annuities when interest rates become random?
This talk presents new stochastic interest models and addresses the above issues from an actuarial perspective. We shall first demonstrate how the notion of deterministic compound interest rates can be generalized to construct stochastic models, and then evaluate the annuities and perpetuities with the stochastic compound interest. Furthermore, a new ruin-theoretic approach will be introduced and applied to price stochastic annuities with a random term of investment.
The talk is self-contained with related techniques and hence will be accessible to audience without background in ruin theory. If you have encountered ruin theory and felt it was not nearly as practical as interest theory, then this is a chance to make you think twice!
Time: 10:00 am
Place: Math & Computing Bldg, Room MC5158
Speaker: Xin Gao
Department of Mathematics and Statistics
York University, Canada
Title: Parameter Estimation and Model Selection in Graphical Models
(Joint work with Peter, X-K Song, Yuehua Amy Wu and Daniel Q. Pu)
Abstract:The recent years have witnessed the increasing interest in the study of graphical models. In this talk, I will discuss two related parameter estimation and model selection problems in graphical models. The first problem is to estimate the concentration matrix of a Gaussian graphical model. We propose to estimate the concentration matrix using the penalized likelihood method with the smoothly clipped absolute deviation (SCAD) penalty. The method leads to a sparse and shrinkage estimator of the concentration matrix. Using proper choice of the regularization parameter, the proposed method automatically and consistently selects the true graphical structure and produces estimator that is as efficient as the oracle estimator. We further establish the consistency of the BIC criterion to identify the true graphical structure when used with the SCAD penalty function. The second problem is regarding the graphic model with multivariate hidden Markov structure. For such high-dimensional data with complicated dependency structure, we propose to use composite likelihood approach and especially we develop COMP-EM algorithm to perform the parameter estimation in the presence of incomplete data. The composite likelihood based information criterion is employed to select the best network structure.
Time: 3:00 pm.
Place: Math & Computing Bldg, Room MC5158
NOTE: NOT THE USUAL TIME OR DAY
Speaker: Prof. Takis Konstantopoulos
Heriot-Watt University and the Maxwell Institute for Mathematical
Sciences, Edinburgh
Title: SPQR (Skorokhod, Palm, Queueing, and Reflection)
Abstract: The Skorokhod reflection problem, originally introduced as a means for constructing solutions to stochastic differential equations in bounded regions, has found applications in many areas of probability, for example in queueing-like stochastic dynamical systems; its uses range from methods for proving limit theorems to representations of local times of diffusions and control. In this talk, I will present several applications, e.g. to Levy stochastic networks and to queueing-like systems driven by local times of Levy processes, and give an order-theoretic approach to the problem by extending the domain of functions involved from the real line to a fairly arbitrary partially ordered set. I will also discuss how Palm probabilities can be used in connection with the Skorokhod problem to obtain information about stationary solutions of certain systems.
Time: 10:00 am
Place: Math & Computing Bldg, Room MC5158
Speaker: Patrick Brown
Cancer Care Ontario
Title: Spatial Models for Cancer in Ontario
Abstract: Spatial models are becoming widely used for disease mapping and for detecting regions with greater than expected rates of a disease. Markov random field models and Bayesian inference offer a computationally feasible solution for modelling a latent spatial random process with Poisson distributed incidence counts. Using these models for cancer in Ontario presents a number of opportunities and challenges. The comparably fine resolution afforded by postal codes enables small area analysis and identification of short scale spatial dependence. However, working on these scales requires overcoming mismatches between census dissemination areas and postal codes. Important covariates such as household income are suppressed in regions of very small population. The extreme irregularity of regions, with census regions in the countryside being much larger than those in towns, also presents a problem. This talk will show a spatial analysis of lung cancer rates in Essex county, Ontario, and discuss solutions to the problems presented when working at the small-area level.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5158
Speaker: Charles Dugas
Universite de Montreal
Title: Pointwise exact bootstrap distributions of ROC curves
Abstract:The use of ROC curves, as a tool to assess the performance of binary classifiers, has been traced back to World War II. Nowadays, areas of application of ROC curves are wide-ranging: medical and social sciences, engineering, data-mining, and machine learning. ROC curve analysis can be enhanced if dispersion measures (confidence intervals or regions) for the performance of a classifier are provided. When choosing between classifiers, a process known as model selection, dispersion measures are to be computed for the difference between two ROC curves. In this talk, I will review some of the solutions that have been proposed to address these two issues and present our results in deriving pointwise exact bootstrap distributions for ROC curves and for the difference between two ROC curves, from which we derive dispersion measures.
Time: 4:00 pm.
Speaker: Philippe Artzner
Universite Louis Pasteur
Tittle: Risk Measures and Efficient Use of Capital
Abstract: This paper is concerned with clarifying the link between risk measurement and capital efficiency. For this purpose we introduce risk measurement as the minimum cost of making a position acceptable by adding an optimal combination of multiple eligible assets. Under certain assumptions, it is shown that these risk measures have properties similar to those of coherent risk measures. The motivation for this paper was the study of a multi-currency setting where it is natural to use simultaneously a domestic and a foreign asset as investment vehicles to inject the capital necessary to make an unacceptable position acceptable. We also study what happens when one changes the unit of account from domestic to foreign currency and are led to the notion of compatibility of risk measures. In addition, we aim to clarify terminology in the field.
Time: 2:00 pm.
Place: Math & Computing Bldg, Room MC5136
Speaker: Anup Dewanji
Indian Statistical Institute, Kolkata, India
Tittle: Estimation of Quality Adjusted Lifetime Distribution in Simple Illness-Death Model
Abstract: When patients experience several health states in their lifetime, the quality adjusted lifetime (QAL) of a patient is defined as the weighted integral of the time spent in successive health states, where weights represent `quality'. In this work, we consider estimation of QAL distribution in a simple illness-death model. The common methods transform the lifetime data in QAL scale and estimation is based on this transformed data. There are several problems with this approach including non-applicability when some transitions are unobserved. The main idea of this work is to derive the theoretical distribution of QAL first and then replace the parameters in this theoretical expression by their estimates obtained by standard techniques of survival analysis. We consider both parametric and nonparametric estimation and also include covariate analysis.
Time: 2:00 pm.
Place: Math & Computing Bldg, Room MC5136
Speaker: Ping Yan
Public Health Agency of Canada
Title: Unifying Statistical Inference and Mathematical Dynamic Models, Illustrated by Data from a Mumps Outbreak
Abstract:To study the transmission of infectious diseases, mathematical dynamic models take into account the biological, clinical and environmental aspects. They usually involve large number of parameters.To fit models to data, parameters are often assigned by adopting results from other studies, or occasionally simply based on "belief", because the number of parameters tend to be large and cannot be all identified from the same data. To be mathematically tractable, many of the models implicitly assume that all the time durations between pairs of successive events in the system are exponentially distributed. Models with non-exponential distributions are more realistic but involve a systems of Volterra renewaltype integro-differential equations. Not only they introduce more
parameters and make fitting model to data even more challenging, but also involve convolution terms that make parameters unidentifiable in statistical sense. On the other hand, statistical models are designed to be data dependent, involving large number of data but low dimension of the parameter space. Parameters tend to take into account on one or few specific aspects of the system instead of the whole system. Very often theyare used to fit models to data and make short term predictions, whereas parameters may be detached from any biological meaning.
These two approaches are regarded by many as different paradigms rather than a continuous modelling spectrum. They are published in different selection of journals and use different terminology. I present a "success story" of unifying statistical inference and mathematical transmission models in a single analysis. Data are from a mumps outbreak that took place in a post-secondary institution in eastern Canada between Feb. 2007 and Feb. 2008. The key difficulty that has been overcome is the identification of the otherwise unidentifiable parameters involved in the
convolution terms in the integro-differential equations . This is achieved by using two theoretical results of Yan (Journal of Theoretical Biology, 2008).
In this presentation, I will present some statistical inferences conducted for:
1. the distribution of the serial interval, defined as the period from the symptom onset in one case to the symptom onset in a second case directly infected from the first case;
2. the distribution of the duration from the symptom onset to the presentation to medical services;
3. back-calculation to establish a time-series of average new infections per time unit using reported data based on date of symptom onset.
Combining the statistical analyses and the results in Yan (2008), one is able to de-convolute the incubation period into the latent period and the infectious period prior to the onset of symptoms. I present a method to identify all the parameters involved for these distributions as well as the reproduction number, one of the most used parameters in mathematical biology. Then I present a model based on a system of Volterra integro-differential equations . The model structure and disease transmission parameters are determined from statistical inferences. Sensitivity analyses are conducted for the environment, such as (i) the initial proportion of infected individuals in the population that started the outbreak and (ii) the average number of new susceptibles joining the"currently" susceptible population per time unit.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5158
Speaker: Catherine Donnelly
University of Waterloo
Title: Convex duality, regime-switching and a portfolio selection problem
Abstract: Mean-variance portfolio optimization problems have been studied for over 50 years. The market model in which these problems are framed have become increasingly more sophisticated in a bid to capture actual market behaviour.
Regime-switching market models are one of the latest attempts. They allow the market to switch between a finite number of regimes, or states, using a Markov chain to model this. However, in most of these regime-switching market models, the market parameters on which the stock price processes depend are deterministic functions within regimes. This prevents the use of stochastic volatility models.
We propose a regime-switching model in which the market parameters are completely random processes. We solve a mean-variance portfolio optimization problem with portfolio constraints in this regime-switching model, showing that an optimal portfolio exists. We use a convex duality method to solve the problem. We also characterize the optimal portfolio in terms of the market parameters and the solution to the dual problem.
We also discuss the canonical martingales associated with the regime-switching Markov chain, which is a continuous-time, finite state Markov chain. We present a martingale representation theorem for processes which are square-integrable martingales with respect to the filtration generated jointly by a Brownian motion and the Markov chain.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5158
Speaker: Raj Bhansali
Department of Mathematical Sciences,
University of Liverpool
Title: Frequency Analysis of Chaotic Intermittency Maps with Slowly Decaying Correlations
Abstract: Established stochastic models for discrete-time long-memory processes are linear and Gaussian and commonly require that the dth fractional difference, 0 < d < 0.5, of the process has short memory; if −0.5 < d < 0, the process is said to have an intermediate memory. Chaotic intermittency maps provide alternative non-linear, non-Gaussian models for both these class of processes. An asymptotic expression for the rate at which the correlations of symmetric cusp map decay is developed and the class of extended symmetric cusp maps is introduced. The small frequency asymptotics of the polynomial, cusp and logarithmic maps are investigated, and it is shown that these maps can produce spectra with d = 0.5 on the one hand and d = 0 on the other hand and yet the corresponding processes are stationary and have long-memory. Asymptotic expressions are also derived for studying the bias of the small-frequency periodogram ordinates with these maps. Finite sample behaviour is examined by a simulation study.
Time: 1:30 pm.
Place: Math & Computing Bldg, Room MC5158
Speaker: A. Thavaneswaran
Department of Statistics, University of Manitoba
Title: Inference for Volatility Models
Abstract: Accurate estimates of volatility parameters are needed in option pricing. Generalized Autoregressive Conditional Heteroscedastic (GARCH) models and Random Coefficient Autoregressive (RCA) models have been used for volatility modelling. Following Thompson and Thavaneswaran(1999) combined estimating functions are used to estimate the parameters in the volatility models. It turns out that the combined estimating function is more informative for autoregressive processes with GARCH errors and for RCA models. The combination of the least squares (LS) estimating function and the least absolute deviation (LAD) estimating function with application to GARCH model error identification is discussed as an application. Recursive estimation for stochastic volatility models and GARCH models are also discussed in some detail.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5136B
Speaker: George Yin
Department of Mathematics, Wayne State University
Title: Switching Diffusion Processes
Abstract: In this talk, we report some of our recent work on switching diffusion processes in which continuous dynamics and discrete events coexist. First, motivational examples arising from finance, singular perturbed Markovian systems, and manufacturing will be mentioned. Then we recall the notion of recurrence and regularity. After necessary and sufficient conditions for recurrence are provided, ergodicity will be examined, and stability will be studied.
Time: 11:00 am.
Place: Math & Computing Bldg, Room MC5158
Speaker: Rachel Altman
Department of Statistics and Actuarial Science, Simon Fraser University
Title: Efficient Designs for Multiple Sclerosis Clinical Trials
Abstract:Multiple sclerosis (MS) is a debilitating, incurable disease of the central nervous system. Symptoms include problems with vision, coordination, sensation, gait, and bowel and bladder function, as well as lesions on the brain and spinal cord. The search continues for improved treatment and management of symptoms. One aspect of this search is the design of efficient clinical trials. In this talk, we present lesion count data from magnetic resonance imaging (MRI) scans from a collection of previous trials. The counts are longitudinal, and are characterized by the presence of many zeroes and a high degree of variability across patients. We show how a mixed hidden Markov model (MHMM) can be used to describe these data, and discuss model selection methods. We then outline our results from a simulation study based on this model. In particular, we compare the performance of the maximum likelihood estimator of the treatment effect (assuming our longitudinal model) to typical estimators derived from independent summary statistics for each patient. We conclude with design recommendations based on each estimator.
This is joint work with John Petkau and Dean Vrecko.
NOTE: For an introduction to MHMMs, graduate students (and others) may find it helpful to read the following paper beforehand:
http://stat.sfu.ca/~raltman/myinfo/JASA2007.pdf.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5136
Speaker: Xin He
College of Public Health, Ohio State University
Title: Semiparametric Analysis of Multivariate Panel Count Data
Abstract: Multivariate panel count data frequently occur in periodic follow-up studies that involve several different types of recurrent events of interest. In many applications, these recurrent event processes can be correlated and it may not be easy to accommodate the dependence structures. In this talk, I will present a class of marginal mean models that leave the dependence structures for related types of recurrent events completely unspecified. Some estimating equations are developed for inference and the resulting estimates of regression parameters are shown to be consistent and asymptotically normal. Simulation studies are conducted for practical situations and the methodology is applied to a motivating cohort study of patients with psoriatic arthritis.
This talk is based on joint work with Dr. Xingwei Tong at Beijing Normal University, Dr. (Tony) Jianguo Sun at University of Missouri, and Dr. Richard Cook at University of Waterloo.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5136
Speaker: Sanjoy Sinha
School of Mathematics and Statistics, Carleton University
Title: Robust methods for incomplete clustered correlated data
Abstract: The EM algorithm is a commonly used iterative method for analyzing incomplete data with generalized linear mixed models. The ML estimators obtained from the EM method are generally sensitive to outliers or departures from the underlying assumptions. In this talk, I will discuss some robust methods for analyzing dependent data with missing responses arising from a nonignorable missing-data mechanism. These robust methods are developed using the notion of the EM method, and are useful for downweighting any influential points in the observed data when estimating the model parameters. To avoid computational problems involving irreducibly high-dimensional integrals, a Monte Carlo Newton-Raphson algorithm based on a Markov chain sampling technique is adopted. I will discuss the computational issues of the robust methods using some illustrative examples, and will also present some numerical results obtained from a simulation study.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5136
Speaker: Yufeng Liu
Department of Statistics and Operations Research and Carolina Center for Genome Sciences, University of North Carolina at Chapel Hill
Title: The large margin unified machine: a bridge between hard and soft classification
Abstract: Margin-based classifiers have been popular in both machine learning and statistics for classification problems. Among numerous classifiers, some are hard classifiers and some are soft ones. Soft classifiers explicitly estimate the class conditional probabilities and then perform classification based on estimated probabilities. In contrast, hard classifiers directly target on the classification decision boundary without producing the probability estimation. These two types of classifiers are based on different philosophies and each has its own merits. In this talk, instead of making a choice between hard and soft classification, we propose a novel family of large-margin classifiers, namely large-margin unified machines (LUMs), which cover a broad range of margin-based classifiers including both hard and soft ones. By offering a natural bridge from soft to hard classification, the LUM provides a unified algorithm to fit various classifiers and hence a convenient platform to compare hard and soft classification.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5136
Speaker: Peter Kim
University of Guelph
Title: Multivariate Topological Data Analysis
Abstract: We examine the estimation of a signal embedded in white noise on a compact manifold. A sharp asymptotic minimax bound is determined under the sup-norm risk over Holder classes of functions and generalizes similar results available for spheres in various dimensions. The estimation allows for the development of a statistical Morse theory using the level sets of the estimated function and together with the sup-norm bound allows the bounding of the Hausdorff distance in a persistence diagram in computational algebraic topology. Time permitting, applications to multivariate data analysis will be discussed.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5158
Speaker: Jeffrey Rosenthal
Department of Statistics, University of Toronto
Title: Adaptive Markov Chain Monte Carlo Algorithms
Abstract: Markov chain Monte Carlo (MCMC) algorithms are often used to sample from complicated posterior distributions. A wide variety of MCMC schemes and settings are available, and it can be difficult to choose among them. One possibility is to have the computer automatically "adapt" the algorithm while it runs, in an attempt to improve efficiency. However, natural-seeming adaptive schemes can destroy the ergodicity properties necessary for MCMC to be valid. In this talk, we review adaptive MCMC, and explain how it can fail even on very simple examples. We then present a theorem which gives conditions ensuring ergodicity, and apply it to several high-dimensional adaptive Metropolis and Metropolis-within-Gibbs examples. (Joint work with G.O. Roberts.)
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5136
Speaker: Shoja Chenouri
Department of Statistics and Actuarial Science, University of Waterloo
Title: Center-outward ranks and multi-sample tests in presence of random right censoring
Abstract: In this talk, I will consider several related problems. Beginning with multi-sample scale rank tests for multivariate data, I will present a percentile modification of these tests for possible improvements in their power. I will adopt these tests to compare two or more multivariate survival functions in presence of random right censoring. For univariate data, I will show that, when the hazard functions are not proportional and / or censoring rate is very high, the proposed tests outperform weighted log-rank tests. The proposed tests will be illustrated through simulations studies.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room MC5136
Speaker: Cecilia Cotton
Department of Biostatistics, University of Washington
Title: Inference for Treatments Targeting Control of an Intermediate Measure
Abstract: A dynamic treatment regimen is a rule or set of rules which define how a subject's treatment at repeated visits depends on their evolving history of time-dependent covariates. For observational data, survival under a particular regimen can be consistently estimated by artificially censoring subjects when they are no longer adherent to the regimen and then weighting subjects by the inverse probability of remaining uncensored. The problem of comparing the causal effects of multiple treatment regimens on survival is complicated by the fact that subjects may have been adherent to multiple regimens at once.
In this talk I will present new methods that allow for inference in this setting. First, I consider a data augmentation method in which regimen membership is stochastically imputed many times and analysis results are summarized appropriately. Second, I propose a ãcloningä methodology in which in which each subject is included in the analysis twice and their follow-up data is examined under adherence to each regimen. A marginal structural Cox proportional hazards model or log rank test with an appropriate variance estimate can be used to compare survival. Finally I will discuss work in progress to allow for more flexible adherence structures such as non-monotonic adherence and/or cross-over between treatment regimens.
These methods will be illustrated through simulation results and an analysis comparing epoetin therapy regimens with different target hemoglobin ranges in a cohort of hemodialysis subjects.
Time: 4:00 pm.
Place: Math & Computing Bldg, Room 5136
Speaker: Fabrizio Ruggeri
CNR IMATI (Italy)
Title: Some Results in Bayesian Reliability
Abstract:
We review new results in different areas of Bayesian reliability in
which the author has been working recently.
The first part (in cooperation with Fernanda D'Ippoliti) will consider
stochastic modelling of cylinder liners wear in a marine diesel
engine. Ship Diesel engines are requested to have high reliability and
availability levels. A major factor in determining failure of
heavy-duty Diesel engines is the ring/liner wear. In high power Diesel
marine propulsion engines maximum wear usually occurs in the top
region of the cylinder liner, which is subject to high
thermomechanical and tribological stresses that produce relevant early
local damages. The talk will present a stochastic differential
equation modelling the wear process. The model can be used to perform
condition based reliability estimation and to plan condition based
maintenance activities.
The second part of the talk (in cooperation with Refik Soyer) will
consider, in a context of software reliability, two models which can
describe the case of reliability decay, due to the introduction of new
bugs. Since the introduction of bugs is an unobservable process,
latent variables are considered to take this process in account. The
two models are based, respectively, on a hidden Markov model and a
self-exciting point process with latent variables.
The final part (in cooperation with Antonio Pievatolo) will illustrate
some models, based on nonhomogeneous Poisson processes, used to
describe failures in underground train doors. Data show failure
dependence on two scales: time and kilometers. Different ways of
considering both scales are analysed.
Time: 1:30 pm.
Place: Math & Computing Bldg, Room TBA
[2005] [2006] [2007] [2009] [2010]
Statistics and Actuarial Science
Math and Computer Building
University of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
Main Office: (519) 888-4567 x33550
FAX (519) 746-1875
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Last Modified: Tuesday 5 January 2010
