| Abstracts of Talks
at the 1999 Meeting |
Marc Loizeaux
Department of Statistics
Florida State University"Pose/Location Estimation of Ground Targets"
Our goal is to identify a detected target using image sequences collected through sensors mounted on a moving platform. Motivated by the missile aim-point selection problem, we focus on pose/location (with respect to a fixed coordinate system) estimation in a situation where the sensor is zooming in to the target. The current estimates (based on the images accumulated thus far) are used to steer the sensor towards the target, resulting in an active sensing environment. Taking a Bayesian approach, we define a posterior on the special Euclidean group, modeling target rotation and translation, and define an optimal estimator in the minimum mean squared error sense. This estimator also establishes a lower bound on ATR performance studied against the ambient
noise level at the sensor.
Jonathan S. Hartzel
Department of Statistics
University of Florida"Nonparametric Maximum Likelihood Estimation in Multivariate Generalized
Linear Mixed Models"In this paper we consider nonparametric maximum likelihood estimation in multivariate generalized linear mixed models. Specifically we focus on the cumulative and baseline category logit models that allow for random shifting
in the thresholds. Our approach does not assume a parametric assumption concerning the distribution of the random thresholds and estimates the discrete mixing distribution along with the regression parameters. The
proposed method is an alternative to the common approach of assuming a normal distribution for the random effect. The EM algorithm utilized in fitting the proposed models is outlined and an example with ordinal data is provided.
Blake Whitten
Department of Statistics
Florida State University"Nonresponse in Spatio-Temporal Data"
Methodology for parametric likelihood analysis for missing-data problems in the spatio-temporal setting has lagged behind the corresponding methodology applied to such problems in areas such as IID data, time series, and longitudinal analysis. Often, computational difficulties have prevented progress.
Now, a Monte Carlo version of Meng and Rubin's ECM Algorithm is proposed for application in spatio-temporal missing data problems, provided that the complete data may be modeled as a conditionally-specified Gaussian distribution.
Substituting a Monte Carlo E-Step for the usual matrix calculations, and substituting several CM-Steps for the E-Step of the EM algorithm both ease the computational burden, and should thus permit the profitable analysis of larger space-time data sets.
The new method is justified theoretically and described in practice. A prototype application is also considered. A simulation experiment is proposed in order to investigate the probabilistic properties of MLE's produced by ECM for a particular fixed three-dimensional grid.
Kevin S. Robinson
Department of Statistics
University of Florida"A Graphical Procedure for Evaluating and Comparing Designs for Generalized
Linear Models"Traditional single-valued design criteria from optimal design theory depend on unknown model parameters when applied to generalized linear models. The use of any optimality criteria would therefore require some prior knowledge of model parameters. Approaches to this difficult problem include using Bayesian
and/or sequential designs.In this talk, a graphical technique is presented for evaluating and comparing designs for generalized linear models. The technique provides an assessment of the overall prediction capability of a given design through a visual display of the mean-squared error of prediction. A logistic regression example is presented to illustrate the proposed approach.
Qiang Zhao
Dept. of Math. and Statistics
Uniersity of North Florida"Supplementary p-value rules for Shewhart k-sigma control charts"
In order to improve the sensitivity of a control chart scheme to small shifts in process mean, a supplementary rule for general Shewhart k-sigma control charts using a p-value rule is proposed. The p-value is obtained from the
hypothesis test about the mean based on a moving average of the previous w sample means. A p-value rule for the k-sigma X-bar chart is developed in detail and the joint ARL of the X-bar chart and a p-value rule is derived.
Choices of w, k, n and p-value control limit that produce control schemes with reasonable in-control ARLs are presented. ARL comparisons are made with 3-sigma X-bar chart with runs rules, zone control chart and EWMA chart. It is shown that the X-bar chart with a p-value rule is more effective in detecting small shifts in the mean than runs rules, zone control chart and is comparable to the EWMA chart.
Mark D. Soskin
Associate Professor of Economics
University of Central Florida"Integrating Computer Software into Business Statistics Service Courses:
Barriers and Strategies in Successful Implementation"
Effective learning in business statistic service courses requires a well-conceived integration of computer software. However, statistical education literature describes many pitfalls in course redesign and implementation.
Among the dangers and barriers commonly cited are time limitations, uncertainties in classroom venues and class sizes, variation in student computer literacy and access to software, software limitations and idiosyncrasies, and superficial, cookbook learning. This paper describes useful strategies to overcome these and other design and implementation difficulties. The proposed, holistic methods also tap into some of the enormous potential benefits of computer integration, such as interactive case analysis and reduction in computational drudgery. Integration strategies are illustrated by actual classroom activity and course material examples. The paper concludes with a discussion of remaining barriers and controversial issues still in need of professional consensus.
Sanford Weisberg
Department of Applied Statistics
University of Minnesota"Graphical Methods for Binary Regression"
In simple regression, the usual graph of the response versus the predictor contains virtually all the information available about the regression problem, and it therefore provides a good summary of the problem. In
regression with a binary response, this graph is not particularly useful because the response is only a zero or a one. After a brief review of binary regression basics, the relationship between graphs and logistic regression
models will be derived and discussed. More general ideas for exploring binary regression through graphics are then presented.
Jayaram Sethuraman
Department of Statistics
Florida State University"Conformation in Metric Pattern Theory"
The phenomenon of conformation in organic chemistry is the natural tendency of two objects (eg. cancer cells) to
fit snugly together (in other words, to conform or couple) in parts of their geometry. This mathematical study tries to model this phenomenon and shows how such couplings can occur when randomness is present. Suppose that the ideal boundary shapes of two cells are described by {(fi(t),gi(t)), t e [0,1]}, i=1,2, where the t=0 is identified with t=1. Consider approximating the boundaries of the two random cells as lines joining the n points (Xi(t),Yi(t)) for t=j/n, j=1,2,..,n, I=1,2. The region [-r/n,r/n] for t is set aside as the region where the two cells conform and couple. The distribution of the dependent perturbations, {(Xi(t) - fi(t), Yi(t) - gi(t)), t e [0,1]}, is specified by a Gibbs distribution controlled by n and the parameters of dependency and coupling. Both weak and strong dependence can be described by varying these parameters. Initially, we use Gaussian dependence and then show how this can be relaxed. We prove limit theorems to show that the law of large numbers and central limit theorem hold in this problem.These results will be illustrated by graphics visualization of simulations of conformation of two objects, under several choices of the parameters of dependence and coupling.
Shanti Gomatam
Department of Mathematics
University of South Florida"A Moment-based Wavelet Thresholding Scheme for Filtering and Compression"
We propose a moment-based framework for thresholding wavelet coefficients to simultaneously de-noise and compress a noisy signal. Hard and soft thresholding estimators that preserve the moments of the underlying signal are derived. While existing thresholding schemes perform well at high signal-to-noise ratios, the moment-preserving threshold does well at low signal-to-noise ratios. Comparisons with the universal threshold, Stein's unbiased risk, minimax, and the Wiener filter estimates, when two moments are preserved on
the proposed estimator, are carried out. It is observed that the proposed estimator performs comparably with the universal threshold estimator and outperforms the others with respect to the signal to noise ratio of the de-
noised signal. The moment preserving estimator is robust to the inaccuracies in the estimates of the noise variance unlike the universal threshold estimator. In terms of compression ratio, a gain of seven to eighteen times is achieved compared to the universal threshold estimate for the hard and soft thresholding respectively. Results for real-life bio-medical data show that the moment preserving estimate is very promising in terms of de-noising and storage.
W. Michael O'Fallon
Mayo Clinic"Modeling Generalized Attributable Risk"
Attributable risk is a simple but underused concept defined as the percent of cases of a disease which can be "attributed" to a risk factor. This presentation introduces the concept of attributable risk, explores its
mathematical foundation and discusses a generalized model of attributable risk which permits multiple risk factors and covariates to be considered. A software package is discussed which uses computer intensive methods (Bootstrap and Jackknife) to estimate the distribution of the generalized attributable risk model. Finally, an example of the utility of the generalized estimate in explicating stroke risk factors is presented. To obtain a more detailed monograph contact the author at ofallon@mayo.edu , or a co-author, Dr. Michael Kahn at kahn@stolaf.edu . Dr. Kahn can also provide access to the software.