Dissertation Topics

Melissa Bingham

Melissa Bingham's Ph.D. dissertation research stems from a materials science problem originally introduced by Dr. Barbara Lograsso of Ames Laboratory. Of interest to Dr. Lograsso is using the orientation of crystals within metals to determine if two pieces of metal were once one piece, which could potentially have use in forensics. Electron Backscatter Diffraction (EBSD) is the technique used to measure the orientation of the crystals within a piece of metal.

Before research begins on Dr. Lograsso's problem, it is important to investigate the repeatability of the measurements taken by EBSD. The focus is on metals with cubic crystal systems so that the orientations can be represented in 3 dimensions as 3x3 orthogonal rotation matrices. This has led to Melissa's dissertation research which identifies a useful class of distributions on orientations in 3 dimensions.

The basic properties of the class and one-sample likelihood-based inference for one member of the class have been investigated. Application has been made to the motivating case, verifying that the EBSD machine does an adequate job of taking repeat readings on a single metal specimen. Current research involves a Bayesian analysis using this class of distributions. Melissa's Ph.D. advisors are Dr. Stephen Vardeman and Dr. Daniel Nordman.

Jeremy Craft

A Bayesian Approach to the Prediction of Deterministic Functions by Transformation of the Input Domain in Computer Experiments

Collaborating Committee Member: Leslie Moore (LANL)

Kim Mueller

The dissertation topic arose from a need to model the percentage of drivers in different age groups to estimate the level of exposure that is required to calculate and compare crash rates. Methods that are currently being used include using the number of licensed drivers in a state or county and using the estimated annual number of miles driven per year of age obtained through a national survey. However, current methods typically do not account for local driving patterns. Consequently, the goal of this research is to develop a model that will be able to detect differences in age group percentages within a country or state so the model can be used to account for local driving patterns.

The data set that will be used to estimate the percentage of drivers in different age groups will consist of information regarding drivers who are considered not-at-fault drivers in two-vehicle crashes since one can reasonably assume that the not-at-fault drivers constitute a random sample of all drivers. Given the goals of the research and the data set to be analyzed as described above, fitting a Multinomial Markov Random Field (MRF) model to the data currently appears to be the best approach. However, before the Multinomial MRF model can be fitted to the data, the behavior of the model needs to be studied. The RTG partner for this research is the Center for Transportation Research and Education (CTRE) at Iowa State University, Ames, IA.

Adam Pintar

In the area of reliability, we are often presented with binary, or pass/fail data and accompanying covariates, e.g. age. One among possibly many appropriate models is a probit regression model, which is the focus of this particular project. On many occasions, it is of interest to fit a probit regression to available data, and then predict reliability, or probability of passing, at a covariate location outside the range of covariates in the original data, i.e. we wish to extrapolate. With this in mind, and assuming we have more than one covariate, the goal of this project is to choose the form of the linear predictor that predicts reliability well in a user-specified portion of the covariate space. While there are many methods currently in use for choosing the form of a linear predictor, e.g. AIC and BIC, they focus on how well the model fits the data for the observed values of the covariates. Our methodology is more flexible, in that it allows the user to specify where in the covariate space they wish to predict well.