St. Lawrence University
Mathematics, Computer Science and Statistics Department
Abstracts for the MAA Undergraduate Poster Session
San Diego, California -
January 8, 2008
Dennis Lock and Richard Torres
Transformations for Improved Estimation of a Beta-Binomial Rate
Advisor: Michael Schuckers
Abstract: Biometric identification uses personal traits and characteristics such as fingerprints and facial recognition to identify an individual. As technology becomes increasingly digital and security concerns gain in prevalence, this field will continue to grow rapidly. Biometric identification devices are not foolproof; they produce both false acceptances and false rejections. Our study aims to improve the inferential estimation of the false accept rate and the false reject rate. In order to do this we assume the proportions in practice are generated according to a Beta-Binomial distribution. Our aim is to create the optimal parametric confidence intervals for biometric error rates. In particular, we are interested in situations with low error rates (0.001 and lower). Using transformations such as the logit, arcsin of the square root, and Wilson transformations, we evaluate the performance of these confidence interval approaches. We find that the logit and the arcsin of the square root transformations are very similar and all three are better than the traditional Wald confidence interval. Additionally we examine combining the transformations and discover that the best possible transformation is the logit transformation on the Wilson transformation base.
To Be or Knot to Be: A Perspective on Knot Tabulation
Advisor: Maegan Bos
Abstract: This research takes an in-depth look at knot tabulation. Through a newly proposed conjecture, the research permits the removal of permutations of Dowker sequences, which are known to fail to produce knots. This eliminates a substantial amount of sequences that are needed to be tested.
Created: January 21, 2008
Math, CS & Stats. Dept.