Seminars and Colloquia by Series

Thursday, February 26, 2009 - 15:00 , Location: Skiles 269 , Henri Matzinger , School of Mathematics, Georgia Tech , Organizer: Heinrich Matzinger
Last week we saw combinatorial reconstruction. This time we are going to explain a new approach to Scenery Reconstruction. This new approach could allow us to prove that being able to distinguish sceneries implies reconstructability.
Thursday, February 19, 2009 - 15:00 , Location: Skiles 269 , Heinrich Matzinger , School of Mathematics, Georgai Tech , Organizer: Heinrich Matzinger
We explore the connection between Scenery Reconstruction and Optimal Alignments. We present some new algorithms which work in practise and not just in theory, to solve the Scenery Reconstruction problem
Thursday, February 12, 2009 - 15:00 , Location: Skiles 269 , Jiawei Liu , Department of Mathematics & Statistics, Georgia State University , Organizer: Heinrich Matzinger
If viewed realistically, models under consideration are always false. A consequence of model falseness is that for every data generating mechanism, there exists a sample size at which the model failure will become obvious. There are occasions when one will still want to use a false model, provided that it gives a parsimonious and powerful description of the generating mechanism. We introduced a model credibility index, from the point of view that the model is false. The model credibility index is defined as the maximum sample size at which samples from the model and those from the true data generating mechanism are nearly indistinguishable. Estimating the model credibility index is under the framework of subsampling, where a large data set is treated as our population, subsamples are generated from the population and compared with the model using various sample sizes. Exploring the asymptotic properties of the model credibility index is associated with the problem of estimating variance of U statistics. An unbiased estimator and a simple fix-up are proposed to estimate the U statistic variance.
Thursday, January 29, 2009 - 15:00 , Location: Skiles 269 , Yuri Bakhtin , School of Mathematics, Georgia Tech , Organizer: Heinrich Matzinger
This work began in collaboration with C.Heitsch. I will briefly discuss the biological motivation. Then I will introduce Gibbs random trees and study their asymptotics as the tree size grows to infinity. One of the results is a "thermodynamic limit" allowing to introduce a limiting infinite random tree which exhibits a few curious properties. Under appropriate scaling one can obtain a diffusion limit for the process of generation sizes of the infinite tree. It also turns out that one can approach the study the details of the geometry of the tree by tracing progenies of subpopulations. Under the same scaling the limiting continuum random tree can be described as a solution of an SPDE w.r.t. a Brownian sheet.
Thursday, January 15, 2009 - 15:00 , Location: Skiles 269 , Alexey Chervonenkis , Russian Academy of Sciences and Royal Holloway University of London , Organizer:
The uniform convergence of empirical averages to their expectations for a set of bounded test functions will be discussed. In our previous work, we proved a necessary and sufficient condition for the uniform convergence that can be formulated in terms of the epsilon-entropy of certain sets associated to the sample. In this talk, I will consider the case where that condition is violated. The main result is that in this situation strong almost sure oscillations take place. In fact, with probability one, for a given oscillation pattern, one can find an admissible test function that realizes this pattern for any positive prescribed precision level.
Friday, December 12, 2008 - 14:00 , Location: Skiles 269 , Joel Zinn , Texas A&M University , Organizer: Heinrich Matzinger
In this approach to the Gaussian Correlation Conjecture we must check the log-concavity of the moment generating function of certain measures pulled down by a particular Gaussian density.
Tuesday, November 25, 2008 - 15:00 , Location: Skiles 269 , Nizar Demni , University of Bielefeld , Organizer: Heinrich Matzinger
We will introduce the Dunkl derivative as well as the Dunkl process and some of its properties. We will treat its radial part called the radial Dunkl process and light the connection to the eigenvalues of some matrix valued processes and to the so called Brownian motions in Weyl chambers. Some open problems will be discussed at the end.
Thursday, November 20, 2008 - 15:00 , Location: Skiles 269 , Jian-Jian Ren , Department of Mathematics, University of Central Florida , Organizer: Heinrich Matzinger
So far, likelihood-based interval estimate for quantiles has not been studied in literature for interval censored Case 2 data and partly interval-censored data, and in this context the use of smoothing has not been considered for any type of censored data. This article constructs smoothed weighted empirical likelihood ratio confidence intervals (WELRCI) for quantiles in a unified framework for various types of censored data, including right censored data, doubly censored data, interval censored data and partly interval-censored data. The 4th-order expansion of the weighted empirical log-likelihood ratio is derived, and the 'theoretical' coverage accuracy equation for the proposed WELRCI is established, which generally guarantees at least the 'first-order' accuracy. In particular for right censored data, we show that the coverage accuracy is at least O(n^{-1/2}), and our simulation studies show that in comparison with empirical likelihood-based methods, the smoothing used in WELRCI generally gives a shorter confidence interval with comparable coverage accuracy. For interval censored data, it is interesting to find that with an adjusted rate n^{-1/3}, the weighted empirical log-likelihood ratio has an asymptotic distribution completely different from that by the empirical likelihood approach, and the resulting WELRCI perform favorably in available comparison simulation studies.
Friday, November 14, 2008 - 14:00 , Location: Skiles 255 , Sayan Mukherjee , Department of Statistical Science, Duke University , Organizer: Heinrich Matzinger
Let X=(X_1,\ldots,X_n) be a n-dimensional random vector for which the distribution has Markov structure corresponding to a junction forest, assuming functional forms for the marginal distributions associated with the cliques of the underlying graph. We propose a latent variable approach based on computing junction forests from filtrations. This methodology establishes connections between efficient algorithms from Computational Topology and Graphical Models, which lead to parametrizations for the space of decomposable graphs so that: i) the dimension grows linearly with respect to n, ii) they are convenient for MCMC sampling.
Thursday, November 13, 2008 - 15:00 , Location: Skiles 269 , Anssi Yli-Jyrä , Helsink University , Organizer: Heinrich Matzinger
Many context-free formalisms based on transitive properties of trees and strings have been converted to probabilitic models. We have Probabilistic Finite Automaton, Probabilistic Context Free Grammar and Probabilistic Tree Adjoining Grammars and many other probabilistic models of grammars. Typically such formalisms employ context-free productions that are transitively closed. Context-free grammars can be represented declaratively through context-sensitive grammars that analyse or check wellformedness of trees. When this direction is elaborated further, we obtain constraint-based representations for regular, context-free and mildly-context sensitive languages and their associated structures. Such representations can also be Probabilistic and this could be achieved by combining weighted rational operations and Dyck languages. More intuitively, the rational operations are packed to a new form of conditional rule: Generalized Restriction or GR in short (Yli-Jyrä and Koskenniemi 2004), or a predicate logic over strings. The conditional rule, GR, is flexible and provides total contexts, which is very useful e.g. when compiling rewriting rules for e.g. phonological alternations or speech or text normalization. However, the total contexts of different conditional rewriting rules can overlap. This implies that the conditions of different rules are not independent and the probabilities do not combine like in the case of context-free derivations. The non-transitivity causes problems for the general use of probabilistic Generalized Restriction e.g. when adding probabilities to phonological rewriting grammars that define regular relations.

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