Department of Mathematical Sciences

School of Natural Sciences and Mathematics

The First UTD Symposium on Statistics and Biostatistics

Honoring the retirement of
Professor John W. Van Ness

The conference will be held on April 30, 2005, at the U.T. Dallas Conference Center Room 1.120

Schedule

8:30 a.m. - Coffee and networking

9:00 a.m. - Introduction and welcome by John Ferraris, Interim Dean of the School of Natural Sciences and Mathematics

9:20 - 10:20 a.m. - Plenary session I and a discussion "Life as a Biostatician" By Lloyd Fisher, University of Washington, Seattle

10:20 - 10:35 a.m. - Coffee break

10:35 - 11:35 a.m. - Plenary session II and discussion "Shape restricted Estimation in the Search for Dark Matter" by Michael Woodroofe, University of Michigan, Ann Arbor

11:35 a.m. - 2:00 p.m. - Lunch

2:00 - 3:00 p.m. - Plenary session III and discussion "Mutual Information in the Frequency Domain" by David Brillinger, University of California, Berkeley

3:00 - 3:15 p.m. - Coffee break

3:15 - 4:15 p.m. - Plenary session IV and discussion "Reporting Uncertainty by Approximating the Likelyhood" by Leon Gleser, University of Pittsburgh

4:15 - 4:30 p.m. - Floor discussion and concluding remarks to all Plenary sessions

4:30 - 6:30 p.m. Contributed paper session

Abstracts

Life as a Biostatistician
by
Lloyd D. Fisher
Professor Emeritus of Biostatistics
University of Washington, Seattle, WA

This talk will be largely non-technical and personal describing my migration from pure mathematics to biostatistics with the majority of the time spent on hopefully interesting experiences as a biostatistician and using this to give views about the desirable traits for a biostatistician and the most appropriate training for this field. Along the way I will mention early times in my career with Professor Van Ness.

Particular emphasis will be placed on the evaluation of new drugs and biologics in human randomized clinical trails with examples from some of my most interesting experiences; e.g. Being on a committee pilloried in the Wall Street Journal as an advisory committee of the Food and Drug Administration decided to sacrifice thousands of American lives on an alter of pedantry. And the comment (intended to be negative) that Medical research has allowed statistics to become the supreme judge of its inventions.

Also my view will be presented about the harm that can come with over adherence to statistical principles without an adequate understanding of a subject matter area. Brief mention of some areas of statistical theory uncertainty in human trials will be made including: active control studies, adaptive analysis and design, and the many problems inherent in safety monitoring.

Mutual Information in the Frequency Domain
by
David R. Brillinger
Professor of Statistics
University of California-Berkeley

Coefficients of mutual information (MI) can prove powerful extensions of classical coefficients of correlation and in particular can prove useful in preparatory work to model building. In this talk MI is studied for bivariate stationary time series with an emphasis on the frequency domain. In a preliminary study an ambient noise seismic data set is analyzed.

Reporting Uncertainly by Approximating the Likelihood
by
 Leon J. Gleser
Professor of Statistics
University of Pittsburgh

The time-honored frequentist way of reporting uncertainty about a parameter is to present a confidence interval. Bayesians prefer to provide a credible interval. The ISO Guidelines attempt to combine these paradigms, but in a way likely to satisfy neither (Gleser, Statistical Science,1998). In the present talk, it is argued that frequentist confidence intervals are particularly inappropriate indicators of post-data uncertainty about a parameter, while Bayesian credible intervals would be calculated differently by different Bayesians.

Further, it has often been pointed out that one cannot directly combine such intervals in meta-analysis. In contrast, the likelihood functions from independent studies can be easily combined, leading many scientists (notably, Enrico Fermi) to suggest using the likelihood function as a summary of the post-data uncertainty concerning the parameter. The likelihood function permits Bayesian inference, and also can be used to obtain large-sample frequentist confidence intervals based on the maximum likelihood estimator. One difficulty is that the likelihood function may not be expressible in a compact, easily- usable mathematical form suitable for publication. Indeed, the likelihood function in mixture models (and other complex models) may only be computable for individual values of the parameter. One possible solution to this problem, which is currently under investigation by my student Ahmet Sezer, is to use regression software to approximate the logarithm of the likelihood using a standard piecewise polynomial with a minimal number of parameters. This has the advantage that the error of approximation is also computed by the regression program and can be reported along with the approximation. In large samples, central limit and saddlepoint approximation theory suggests that just two or three knots may be needed, with the approximating polynomial being quadratic inside and linear outside of the knots. With such an approximation, it is easy to construct confidence and credible regions for the parameter(s).

"Shape Restricted Estimation in the Search for Dark Matter" (click for PDF file)
by
Michael B. Woodroofe
L.J. Savage Professor of Mathematics and Statistics
University of Michigan

Parameter Estimation for A Modified Weibull Distribution based on Progressively Type-II Censored Data
by
Hon Keung Tony Ng
Southern Methodist Univeristy, Dallas, TX

In this talk, I will first introduce a modified Weibull distribution proposed by Lai, Xie and Murthy (2003, IEEE Trans. Reliab.) and discuss its distributional properties as well as the relationships to other distributions. Then, two estimation procedures for the model parameters - least-square fit of multiple linear regression and maximum likelihood estimation - based on a progressively Type-II censored sample will be discussed. The estimators based on least-square fit of multiple linear regression are compared with the MLE via Monte Carlo simulations. Some recommendations are made from the results of a Monte Carlo simulation study and a numerical example is presented finally.

Interval Estimation for a Change in the Hazard Rate with Staggered Entry
by
Dong-Yun Kim
Illinois State University, Normal, IL

We construct a confidence interval for a change in hazard rate of the patient's survival distribution when the patients enter the trial at random times. We show that the local- likelihood ratio process converges weakly to a certain process and obtain the maximum distribution of the process which does not depend on the change point. We illustrate the method using the Stanford Heart Transplant data. Using the Monte Carlo simulation we compare the limiting distribution to the empirical density function and discuss the empirical coverage probability of the confidence interval.

Estimation of New Epidemic Trends using a Poisson Gradual Change Model
by
Ryan Gill
University of Louisville, Louisville, KY

This talk discusses a gradual change model for the Poisson distribution with emphasis on the identifiability, uniqueness, and existence of estimators produced by maximum likelihood. This model is used to analyze data from the SARS epidemic of 2003. In addition, procedures for detecting multiple changes are discussed and applied to this data set.

Risk evaluation for sequentially planned statistical procedures
by
Claudia Schmegner
DePaul University, Chicago, IL

Sequential planning proposes a compromise between 'pure' sequential analysis and classical statistics by allowing sequential sampling in groups of variable sizes. Optimality of sequential plans is evaluated in terms of a suitable risk function that balances an observation cost and a group cost.

Although risk evaluation is a challenging problem in sequential planning, risk functions of sequentially planned probability ratio tests (SPPRT) can be obtained as roots of certain functional equations. Explicit solutions are derived for SPPRT on a lattice, allowing practitioners to compare exact risks and choose an optimal procedure.

It is shown that the theory of SPPRT on a lattice can be applied to a number of common discrete and continuous underlying distribution families.
Typically, a certain relationship between the parameter under the null hypothesis and under the alternative needs to be met. Accurate approximations are always available even if this condition is not satisfied exactly.

Use of Multiple Rankers in Judgment post-stratification
by
Xinlei (Sherry) Wang
Southern Methodist University

Judgment post-stratification is a method of data collection in which the members of a random sample are stratified after selection by ranking each one among its own randomly chosen comparison sample. The original random sample units are measured, whereas those in the comparison sample are not. An estimator of the mean can be constructed from this sample that is similar to that from a ranked set sample, and has similar properties. That is, if ranking is reasonably accurate and measurement is expensive compared to ranking, this estimation procedure improves efficiency in estimation of the mean. In this paper, we develop methods for making use of judgment ranks from more than one ranker in estimation of the mean. We show that when rankers are not identical, there can be considerable benefit in having more than one. Surprisingly, even if one ranker is perfectly accurate, the presence of imperfect information can also be an advantage in estimation.

For More Information

Michael Baron

  • Updated: June 7, 2005