The Lloyd Roeling UL Lafayette Mathematics Conference is held annually during the fall semester on the UL Lafayette campus. The conference is named in memory of Lloyd Roeling who was instrumental in establishing and nurturing this regional conference. The conference has been held annually, save two hurricane years, since 1970. The topic of the conference rotates among algebra, applied mathematics, statistics, and topology.

SCHEDULE

TITLES AND ABSTRACTS

Reference Intervals and Reference Regions With Applications in Laboratory Medicine
Thomas Mathew
Department of Mathematics and Statistics
University of Maryland, Baltimore County Campus
Baltimore, Maryland
mathew@umbc.edu
(Joint with Xiaoyu Dong)

In the field of laboratory medicine, reference intervals and reference regions represent a range of values that a physician can use in order to interpret the test results of a patient. For a given test, the reference interval (or region) is obtained based on test results from healthy individuals. A test result outside the reference region may be indicative of a disease. In the case of univariate test results from a healthy population, a 95% reference interval is simply the interval from the 2.5th to the 97.5th percentiles of the distribution of the test results. Since these percentiles are unknown, a natural approach is to obtain an interval, based on a random sample, that will contain the range from the 2.5th to the 97.5th percentiles of the underlying distribution. Such an interval is referred to as a statistical reference interval, or a central tolerance interval. A statistical reference region (or a central tolerance region) can be similarly defined for a multivariate population. In the talk, the construction of central tolerance intervals and regions will be described for univariate and multivariate normal populations, and also for linear regression models. Some examples from laboratory medicine will be used to illustrate the applicability of the results.

Robust Estimation in Simple Random Sampling
Evrim Oral
Biostatistics Program
LSUHSC School of Public Health
New Orleans, LA
eoral@louisiana.edu
(Partially joint work with Cem Kadilar)

In sampling theory when the correlation between study and auxiliary variables is positively high, the classical ratio estimator is the most practicable estimator to estimate the population mean. Sisodio and Dwivedi (1981), Upadhyaya and Singh (1999), Ray and Singh (1981) and Kadilar and Cingi (2004) suggested to use population information of the auxiliary variable to increase the efficiency of the ratio estimator. By adapting robust regression approaches to the Kadilar-Cingi estimators (KCE), we obtain novel ratio estimators. We compare the adapted estimators both with KCE and the classical ratio estimator. We also introduce a simpler ratio-type estimator based on the order statistics of a simple random sample. We show that this new estimator is considerably more efficient than the traditional ratio estimator under non-normality, and remarkably robust to data anomalies such as presence of outliers.

Question Answering Systems
Nicholas Ruiz
Senior Software Architect
Center for Business & Information Technologies
University of Louisiana at Lafayette
Lafayette, LA
nruiz@louisiana.edu

Question Answering (QA) is a fast growing field in both research and industry. In the past couple of years we have witnessed a trend in television commercials for mobile question answering services, a new search engine that promised to cut through the clutter, and a supercomputer best two human champions on a question based game show. I will discuss three of the main approaches to question answering: i) community based question answering systems, ii) database-driven knowledge-bases, and iii) open-domain question answering systems. Open-domain question answering systems utilize statistical features in order to extract and select answers from data on the internet. I will discuss several of these features and how they utilize statistics to select potential answers. I will compare two evolutionary learning algorithms that can be used to select or weight features when tuning a question answering system.

A New Family of Bivariate Copulas Generated by Univariate Distributions
Xiaohu Li
Department of Mathematics
University of New Orleans
New Orleans, LA
mathxhli@hotmail.com

A new family of copulas generated by a univariate distribution function is introduced, we discuss the relations between this copula and other well-known ones. The new copula is also applied to a real data set on insurance claims.

Inferences On A Skew-Normal Distribution
Nabendu Pal
Mathematics Department
University of Louisiana at Lafayette
Lafayette, LA
nxp3695@louisiana.edu

It is a common practice among applied researchers to assume normal distribution for naturally occurring data over the real line. But often one is not sure about the assumption of normality for various reasons, including the fact that the standard goodness of fit tests are not effective enough always, especially for small sample sizes. In such a scenario one would be better off by starting with a more versatile skew-normal distribution which is defined over the whole real line, and is a natural generalization of the usual normal distribution. This paper deals with the standard skew-normal distribution which can reduce to the standard normal distribution if the skew parameter takes the value zero. Depending on the value of the skew parameter, the standard skew-normal distribution can be either positively skewed, symmetric (standard normal), or negatively skewed. This paper is devoted to various estimation and hypothesis testing methods for the skew parameter which, to the best of our knowledge, is the first comprehensive work in this direction.

Score and Fiducial Confidence Intervals for the Difference Between Two Poisson Means
Meesook Lee
South Louisiana Community College
Lafayette, LA
statmslee@gmail.com
(Joint with K. Krishnamoorthy)

The problem of estimating the difference between two Poisson means is considered. A new score confidence interval (CI), and a fiducial CI for the difference between the means are proposed. The score CI is simple to compute, and it specializes to the classical Wald CI when the sample sizes are equal. Numerical studies indicate that the score CI offers improvement over the Wald CI when the sample sizes are different. Calculation of the fiducial CI involves Monte Carlo simulation, nevertheless, it is more accurate than the score CI in terms of coverage probabilities for small parameter values. Exact properties of the CIs based on the score, fiducial and hybrid methods are evaluated numerically. Our numerical study indicates that the hybrid and score CIs are in general comparable, and the score CI seems to be the best when the expected total counts from both distributions are two or more. The interval estimation procedures are illustrated using two examples.

Dominance Measures for Univariate Distributions
Calvin Berry or Charles Anderson
Mathematics Department
University of Louisiana at Lafayette
Lafayette, LA
cberry@louisiana.edu
statcata@gmail.com

Dominance measures which assign a value between zero and one to pairs of univariate distributions are considered. The use of such pairwise dominance measures for consistent orderings and groupings of collections of univariate distributions is explored.

Information about past conferences.

2011 conference (Statistics)

2010 conference (Algebra)

2009 conference (Topology)

2008 conference (Applied mathematics) Photos

2007 conference (Algebra)

Information about the 2006 conference is not available at this time. We plan to post this soon.

The 2005 conference was cancelled due to Hurricane Katrina.

2004 conference (Statistics)

2003 conference (Applied mathematics)

2002 conference (Algebra)