For more information, contact the Colloquium/Seminar Coordinator, Dr. Hokwon Cho
(To see Math Dept Colloquia/Seminars, click next: Math Dept Seminar)
University of Nevada, Reno
to Hydrology, Climate and Finance
[Abstract] We consider the problem of modeling the joint distribution of the duration, maximum and magnitude of stochastic episodes (events). An event is defined as consecutive observations of a process above (or below) a threshold. Examples of events include growth (or decline) periods of a financial series or climatic or hydrologic episodes, e.g. flood, draught, heat wave, cold spell, etc. Let N, X, and Y describe episodes as their duration (N), magnitude (X) and maximum/peak (Y). The distribution of the vector (N, X, Y) is of direct interest to water management, energy management companies, disaster management, health departments as well as state and federal regulatory agencies. In particular, the probability of extreme events associated with large values of (N, X, Y) are of primary interest. We present the exact joint distribution of the vector (N, X, Y) and its marginals and conditionals, when N has a geometric distribution, X is the random sum and Y is the random maximum of N iid exponential random variables. We also provide error estimates for the computation of probabilities using models from this family. We illustrate the modeling potential of these distributions using hydroclimatic data.
University of Nevada, Las Vegas
Naturally Occurring and Anthropogenic Beryllium in the Workplace
[Abstract] Metal ratios can effectively predict the amount of (non-toxic) natural beryllium (N-Be) that should be found in an inside-facility sample based on the amounts present of other metals characteristic of minerals in background soils. The difference between the total Be measurement and the predicted N-Be for that sample is an estimate of the amount of (toxic) anthropogenic Be (A-Be) present. These A-Be estimates can then be used in determining whether the facility is “clean” using an appropriate decision rule.
Friday, November 16
University of Maryland, Baltimore County
[Abstract] During the last fifteen years or so, generalized P-values have become quite useful in solving testing problems in many non-standard situations. In this talk the notion of a generalized P-value will be explained and its many applications will be presented. The application area will mostly include linear models.
University of Trento, Italy
[Abstract] The concept of regularly varying function is an essential analytical tool for analyzing data in economics and finance, since a remarkable number of regularities, or “laws”, are considered to follow an approximate power law, at least in the upper tail, in these fields. Available estimators of the tail index of a distribution are usually based on extreme order statistics which are often too few to provide exhaustive information on the problem.
In the talk, a different approach, based on a regression-type estimator, which utilizes all sample data will be considered. The method discussed exploits the fact that, under some conditions, the behavior of the distribution function near infinity is reflected in the behavior of the characteristic function near the origin. The approach is semi-parametric as only an assumption about the tail of the distribution is used. Theoretical properties of the estimator, including its bias, variance and asymptotic distribution are derived as well as rules for its practical application.
Washington State University
[Abstract] We consider an m-dimensional vector autoregressive process Zt of integrated order 1, such that Zt = (Y’t ,Xt’)’ where Yt is an my-dimensional vector process of endogenous variables and Xt is an mx-dimensional vector process of exogenous variables with my + mx = m. We assume that there are r cointegrating relations in Zt. Pesaran et al. (2000), Johansen (1992) and Harbo et al. (1998) considered inference of Zt assuming the weak exogeneity of Xt , that is, the nonstationary exogenous variables are not cointegrated. We consider the case where exogenous variables are cointegrated with rank rx < mx. Parameterization and estimation of the model is considered, and the asymptotic properties of the least square estimator and the maximum likelihood estimator are presented. A real data example is provided to illustrate the methods. Finite sample properties of the estimators are also examined through a Monte Carlo simulation.
Feb. 5 – Mar. 5
Department of Mathematics and Statistics
University of Nevada, Reno
Title: Laplace Probability Distributions and Generalizations:
An Excursion Beyond Normality
[Abstract] Skew Laplace distributions, which naturally arise in connection with random summation and quantile regression settings, offer an attractive and flexible alternative to the normal (Gaussian) distribution in a variety of settings where the assumptions of symmetry and short tail are too restrictive. The growing popularity of the Laplace-based models in recent years is due to their fundamental properties, which include a sharp peak at the mode, heavier than Gaussian tails, existence of all moments, infinite divisibility, and, most importantly, random stability and approximation of geometric sums. Since the latter arise quite naturally, these distributions provide useful models in diverse areas, such as biology, economics, engineering, finance, geosciences, and physics. We review fundamental properties of these models, which give insight into their applicability in these areas, and discuss some extensions, including time series and stochastic processes.
Hoffmann-La Roche Inc., NJ
from Health Care
[Abstract] The detection of the change point in sequential data or the detection of the starting/ending point of drop-down in longitudinal data is an important problem in health care application. However, the recent data from diseases spreading or clinical area are so complex that the existing methods may not work well. In this presentation, we discuss several challenging issues in the change-point problems derived from complex data and propose better approaches. In the sequential change point problem from health care surveillance, the baseline might exhibit a systematic pattern from population changes. Furthermore, spatiotemporal surveillance should consider spatial features, and regional data might be correlated. We propose the general framework based on likelihood ratios to deal with such challenging issues. In the change detection problem from the longitudinal data, the data in clinical areas such as blood flow shows a flexible non-linear curve with change points. We consider one approach based on the partial spline model, and propose a modification to generalized cross validation criteria for choosing the smoothing parameter in order to reduce the bias of the change time estimate.
Friday, May 3
[Abstract] Sequential tests have been used commonly in clinical trials to compare treatments. For sequential analysis of right censored survival data with covariate adjustment, several different methods have been studied in the literature. Here I review available methods and present recent development in this topic. Numerical studies will also be presented.