Title: Selecting the threshold through the entropy of the Dirichlet Process when the peaks over threshold method is applied in Extreme value analysis
Speaker: Professor DJ De Waal
Department of Statistics/Mathematical Statistics
Bloemfontein University, South Africa
Abstract:
The choice of the threshold t if the Peaks over Threshold (POT) method is applied to model extreme data through the entropy of the Dirichlet Process (DP) is considered. Davison & Smith (1990) proposed the mean excess function as a way to choose the threshold if the Generalized Pareto Distribution (GPD) is fitted, but it is not very satisfactorily. Various methods for comparison such as minimizing the mean square error
of the Hill estimator and Bootstrap methods exist (Beirlant et al, 2004) to select t, but they are independent of the model. Various models require different thresholds. The predictive density of a future extreme observation is derived from the DP and an application discussed.
Date: Friday, January 20, 2006
Time: 4:00-5:00 pm
Location: 2140 Pennsylvania Avenue, Statistics Library
Title: Phase Changes in Subtree Varieties in Random Trees
Speaker:Professor Hosam M. Mahmoud
Department of Statistics
George Washington University
Abstract: The occurrence of patterns in random objects is an important area of modern research. The prime example is the interest one may have in the number of occurrences of words of a certain length in that text. Applications abound in linguistics where one wishes to analyze grammatical frequencies, or in genetics where one tries to identify genes in strands of DNA. The equivalent and equally important view in random trees is to find patterns (which are trees of a certain size or a certain shape) in a given tree generated randomly. We look at the number of subtrees of a certain size on the fringe of random recursive trees, which have applications in epidemiology, philology, etc., and in random binary search trees, which have applications in computer science.
We consider the variety of subtrees of various sizes and shapes lying on the fringe of a recursive tree. For the number of subtrees of a given size k =k(n) in a random recursive tree of size n, three cases are identified: the subcritical, when k(n)/sqrt(n) tends to zero, the critical, when k(n) is of the exact order sqrt(n), and the supercritical, when k(n)/ sqrt(n) tends to infinity. We show by analytic methods convergence in distribution to 0 in the supercritical case and to normality (of a normalized version of the size) in the subcritical case. We show that the size in the critical case when k/sqrt(n) approaches a limit converges in distribution to a Poisson random variable, and in the case k/sqrt(n) does not approach a finite nonzero limit, the size oscillates and does not converge in distribution to any random variable. This provides an understanding of the complete spectrum of phases and the gradual change from the subcritical to the supercritical phase.
We utilize the same battery of methods to derive similar results for binary search trees. Connections are made to Riccati equations, Polya urns and contraction in metric spaces of distributions and fixed-point equations for distribution functions.
This work is based on papers joint with Chun Su, and Qunqiang Feng, University of Science and Technology of China, and Alois Panholzer, Technical University , Vienna , Austria
Date: Friday, January 27, 2006
Time: 11:00-12:00 noon
Location: 1957 E Street, Room B16
Title: New Monte Carlo Strategies with Applications to Spatial Models
Speaker: Professor Murali Haran
Department of Statistics
Pennsylvania State University
Abstract: Hierarchical Bayes models often result in posterior distributions that present challenges to non-expert users of Markov chain Monte Carlo (MCMC) methods. Two long standing questions are: How long should one run an MCMC algorithm and, once the algorithm is stopped, how accurate are the resulting estimates? I will describe two approaches for
resolving these questions. The first involves the construction of "perfect" or exact sampling procedures for which these questions are moot. Perfect samplers have so far been generally impractical for all but the simplest Bayesian problems; I will explain how one can use perfect samplers for some realistic Bayesian models. The second approach describes how Monte Carlo standard errors for MCMC-based estimates can be computed and used to determine the run length of the algorithm, thereby providing practical and theoretically justified answers to both questions of interest. I will conclude with an application of these methods to some data examples.
This talk is based on joint work with: Brian Caffo ( Johns Hopkins University ), Galin Jones and Ronald Neath ( University of Minnesota ) and Luke Tierney ( University of Iowa ).
Date: Friday, February 10, 2006
Time: 11:00-12:00 noon
Location: 1957 E Street, Room B16
Title :Distributions in the Ehrenfest Process
Speaker : Professor Srinivasan Balaji
Department of Statistics
George Washington University
Abstract
In this talk we will discuss recent results on Ehrenfest processes, which are special cases of Polya processes. Polya process is obtained by embedding a discrete Polya urn process in continuous time. Polya processes give us the best heuristics to approximate and understand the intricate Polya urn models as the discrete process is in general difficult to deal with. Recent work has shown that a class of partial differential equations, related to the corresponding ball addition matrix, governs such processes. However only in some cases these partial differential equations are amenable to asymptotic solution.
After describing the general Polya process, we will restrict our attention to a tenable class of urns that generalize the classical Ehrenfest model. Ehrenfest urns arise in applications to model the exchange of particles in two connected gas chambers. Finally we conclude with some remarks about the connections to pseudo expectation of Markov chains.
The work on Ehrenfest processes is a joint work done with Prof. Hosam Mahmoud in the department of Statistics, GWU, and Prof. Osamu Watanabe of Tokyo Institute of Technology.
Time : 4:00-5:00 – February 24, 2006
Location : 1957 E street, room B16
Title: Statistical Issues in Large-Scale Genetic Association Studies
Speaker: Professor Eleanor Feingold
Department of Human GeneticsStatistics
University of Pittsburgh
Abstract:
New genomic technologies are now making it possible (if not quite affordable) to conduct genetic association studies on a very large scale – up to half a million genetic markers spanning the genome. In some ways these studies are quite statistically routine, but there are also a number of new challenges for biostatisticians in both the design and analysis. This talk is a survey of several areas in which I think there are important statistical problems that have not gotten enough attention. I will give some illustrative research results and discuss some open questions.
Date: March 31, 2006
Time: 11:00-12:00 pm
Location: 1957 E Street, Room B16
Title: Some Aspects of Bayesian and Decision Theoretic Approaches to Statistical Prediction
Speaker: Professor Tapan K. Nayak
Department of Statistics
George Washington University
Abstract:
Prediction is a general statistical inference problem, which covers estimation and many non-standard inference problems as special cases. In the general set up, inferences are to be made about an unknown quantity z based on an observable random vector Y. The unknown quantity z may be fixed or the realized but unobserved value of a random variable Z. In a parametric set up the joint density is assumed to be f_theta (y, z), where theta is an unknown parameter vector. We shall present lower bounds for the MSE of unbiased predictors and a characterization of uniformly minimum MSE unbiased predictors. We shall explore the possibility of reducing a prediction problem under a loss function and a prior distribution to a standard decision theory problem and discuss some admissibility results. We shall also formalize the concept of risk-unbiased for predictors and present a Rao-Blackwell type result. Applications of some general results to prediction in mixed linear models and to finite population sampling will be discussed.
Date: April 14, 2006
Time: 4:00-5:00 pm
Location: 1957 E Street, Room B16
Title: A Semiparametric Approach to Time Series Prediction
Speaker: Professor Benjamin Kedem
Department of Mathematics
University of Maryland
Abstract
Given m time series regression models, linear or not, with additive noise components, it is shown how to estimate the predictive probability distribution of all the time series conditional on the observed and covariate data at the time of prediction. This is done by a certain
synergy argument, assuming that the distributions of the residual components associated with the regression models are tilted versions of a reference distribution. Point predictors are obtained from the predictive distribution as a byproduct. Applications to US mortality rates prediction and to value at risk (VaR) estimation will be discussed.
Time : 11:00-12:00 noon – April 28, 2006
Location : 1957 E street, room B16
The series hosts a seminar about twice a month on current
research topics. The seminar often features an invited
guest speaker and occasionally local faculty members,
students or others affiliated with the department. The
usual time of the seminar is 11:00 a.m. on Fridays. Professor
Reza
Modarres (E-mail : reza@gwu.edu)
is the Seminar Series Coordinator.
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The contact person is Reza Modarres at Reza@gwu.edu or 202-994-6359.
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