PMean: My research contributions to numerical accuracy

The U.S. National Institutes of Health (NIH) has a new biosketch format where they ask you to summarize “up to five of your most significant contributions to science.” Here’s a first draft of my research contributions to numerical accuracy.

At Bowling Green State University, I partnered with an Economics faculty member, James P. Lesage, to study numerical accuracy issues. The major statistical software packages were just being ported to microcomputers and the combination of single precision calculations with the (sometimes) poorly implemented algorithms led to some startling bad results. These publications started with the seminal data set for numerical accuracy, the Longley data set, and looked at a flexible alternative developed by Wampler. We developed an extension to the Wampler data set that could examine near collinearity involving the intercept term and produced new benchmarks for Analysis of Variance. Some of these benchmarks were adopted by the National Institute for Standards and Technology for their Statistical Reference Datasets project. I also produced a couple of pedagogical articles that clearly illustrated how problems with numerical accuracy can arise. The work in this area gave me an early overview of the broad range of statistical software packages available for microcomputers.

Simon SD, Lesage JP. Assessing the accuracy of ANOVA calculations in statistical software. Computational Statistics and Data Analysis 1990: 8(3); 325-332.

Simon SD, Lesage JP. The impact of collinearity involving the intercept term on the numerical accuracy of regression. Computer Science in Economics and Management 1988: 1; 137-152.

Simon SD, Lesage JP. Benchmarking numerical accuracy of statistical algorithms. Computational Statistics and Data Analysis 1988: 7; 197-209.

Simon SD. How to illustrate numerical accuracy problems on any computer. Mathematics and Computer Education 1987: 21(1); 11-15.

Simon SD. To err isn’t only human. Computer Language 1986: 3(3); 71-76.

Lesage JP, Simon SD. Numerical accuracy of statistical algorithms for microcomputers. Computational Statistics and Data Analysis 1985: 3; 47-57.

Here’s a picture of Dr. Lesage, from his website at Texas State University – San Marcos.